Post by: khalil on August 26, 2009, 01:33:46 pm
If Z has the standard normal distribution and Pr(Z< c)= a, where 0<c<3 and 0<a<1, then Pr(|Z|<c) is equal to:
ans. 2a-1
Post by: TrueTears on August 26, 2009, 01:39:09 pm
so since Pr(Z < c) = a
then Pr(Z > c) = 1-a
Using symmetry Pr(Z < -c) = 1-a
Therefore the area between -c and c is 1-(2(1-a)) = 1 - 2 + 2a = 2a - 1.
Post by: khalil on August 26, 2009, 02:51:17 pm
Post by: khalil on August 26, 2009, 08:23:54 pm
Post by: TrueTears on August 26, 2009, 08:26:16 pm
What does the are under a graph represent???????????????????????
Post by: NE2000 on August 26, 2009, 08:31:01 pm
What does the are under a graph represent?
Under a pdf (including a normal distribution curve), it represents the probability
If that's not what you're asking, I empathize with TT
Post by: khalil on August 26, 2009, 08:49:17 pm
Post by: Flaming_Arrow on August 26, 2009, 09:31:15 pm
Post by: khalil on August 27, 2009, 09:49:06 am
Post by: zzdfa on August 27, 2009, 10:00:21 am
Post by: khalil on August 27, 2009, 10:14:00 am
Post by: Flaming_Arrow on August 27, 2009, 03:26:48 pm
so does that mean proportion of one thing and another is the multiple of k?
it means when one thing increases, other thing increases too
Post by: khalil on August 27, 2009, 03:38:33 pm
Show that the prob. of it occuring just twice in three trials is 0.25.
ans.
E=event
N=no event
ENE= 0.5*1*0.5= 0.25
My Question: why is N, 1?
Post by: shinny on August 27, 2009, 04:39:10 pm
At each of a series of trials, the probability of the occurence of a certain event is 0.5, except this cannot occur in 2 consecutive trials.
Show that the prob. of it occuring just twice in three trials is 0.25.
ans.
E=event
N=no event
ENE= 0.5*1*0.5= 0.25
My Question: why is N, 1?
Because it's stated that the event (E) cannot occur in 2 consecutive trials. If E cannot occur, then N must occur, therefore Pr(N)=1.
Post by: khalil on August 27, 2009, 04:42:20 pm
Post by: shinny on August 27, 2009, 04:46:39 pm
I don't understand. I thought if E cannot occur then N would be 1-0.5
How so? The only events available that can happen is E or N. If E cannot occur twice consecutively, and E has already occurred on the first trial, then on the second trial, E cannot occur. If E cannot occur, then the only option left is for N to occur on the second trial, making the probability of N occurring 100%. Can you explain to me how you got 1-0.5 and maybe I could figure out what you don't understand?
Post by: cobby on August 27, 2009, 04:47:19 pm
At each of a series of trials, the probability of the occurence of a certain event is 0.5, except this cannot occur in 2 consecutive trials.I did it this way..
Show that the prob. of it occuring just twice in three trials is 0.25.
ans.
E=event
N=no event
ENE= 0.5*1*0.5= 0.25
My Question: why is N, 1?
First draw a tree diagram of all the possible events, then rule out all the options that have two consecutive occurrences left
Which should be ENE and NEN
Therefore the probabilities are
(0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5) = 0.25
Post by: khalil on August 27, 2009, 07:53:12 pm
I don't understand. I thought if E cannot occur then N would be 1-0.5
How so? The only events available that can happen is E or N. If E cannot occur twice consecutively, and E has already occurred on the first trial, then on the second trial, E cannot occur. If E cannot occur, then the only option left is for N to occur on the second trial, making the probability of N occurring 100%. Can you explain to me how you got 1-0.5 and maybe I could figure out what you don't understand?
Yep i understand know shinny, thanks
Post by: khalil on August 27, 2009, 08:14:46 pm
ans. 76 cents
Post by: Flaming_Arrow on August 27, 2009, 08:47:58 pm
so its 1 and -x
1 = Pr(1) + Pr(3) + Pr(5)
-x = Pr(0) + Pr(2) + Pr(4) or you can just do 1-(Pr(1) + Pr(3) + Pr(5))
now in order it to be fare mean must equal zero
so Pr(1) + Pr(3) + Pr(5) - x(Pr(0) + Pr(2) + Pr(4)) = 0
solve for x
Post by: khalil on August 27, 2009, 09:10:12 pm
A newspaper seller buys papers for 50 cents and sells them for 75 cents, and cannot return
unsold papers.
If the newspaper seller stocks too many papers a loss is incurred. If too few papers are
stocked potential profit is lost because of the excess demand. Let s represent the number
of newspapers stocked, and X the daily demand.
a) If P is the newspaper seller’s profit for a particular stock level s, find and expression
for P in terms of s and X.
ans. 0.75x-0.5s x<s
0.5s-0.25x x>s
Post by: TrueTears on August 27, 2009, 09:11:15 pm
Post by: khalil on August 28, 2009, 02:52:47 pm
Post by: khalil on August 28, 2009, 04:09:20 pm
Post by: TrueTears on August 28, 2009, 04:27:27 pm
Post by: khalil on August 28, 2009, 05:21:45 pm
the assesor's report http://www.vcaa.vic.edu.au/vce/studies/mathematics/methods/assessreports/2007/mm-mmcas1_assessrep_07.pdf fails to mention that +C is included in antideriving. Does this mean we dont have to put +C in?
Also, in the assesor's report they quote 'The instruction ‘hence’ was often ignored,' I don't see the word hence in the question. Can someone explain.
Post by: hyperblade01 on August 28, 2009, 05:24:53 pm
'AN antiderivative' which implies one only. +c kinda makes it general
Badly worded, I'm sure someone else can explain it better
EDIT: 'Use the fact' is the same as 'hence', 'therefore', 'now' etc
Post by: TrueTears on August 28, 2009, 05:29:49 pm
Post by: khalil on August 28, 2009, 05:40:02 pm
Yes hyperblade01 is right, remember the subtle difference b/w THE anti derivative and AN anti derivative.
Interesting. But if I did add C, they can't take off marks, could they?
Post by: TrueTears on August 28, 2009, 05:42:25 pm
Post by: khalil on August 28, 2009, 09:04:59 pm
Post by: TrueTears on August 28, 2009, 09:12:30 pm
Post by: Flaming_Arrow on August 28, 2009, 09:12:40 pm
EDIT: beaten
Post by: khalil on August 28, 2009, 09:30:11 pm
Pr(B)= Pr(B|A)\times Pr(A)+ Pr(B|{A}')\times Pr({A}')
Post by: Flaming_Arrow on August 28, 2009, 09:30:48 pm
Are we supposed to know the law of total probability?
Pr(B)= Pr(B|A)\times Pr(A)+ Pr(B|{A}')\times Pr({A}')
yep
Post by: khalil on August 28, 2009, 09:31:58 pm
Post by: TrueTears on August 28, 2009, 09:32:13 pm
Post by: khalil on August 28, 2009, 09:39:29 pm
Post by: /0 on August 28, 2009, 09:41:13 pm
Post by: Flaming_Arrow on August 28, 2009, 09:43:22 pm
Post by: khalil on August 28, 2009, 09:49:25 pm
Post by: Flaming_Arrow on August 28, 2009, 09:49:44 pm
Ok thanks. Wow, Flaming_Arrow, did you prepare those diagrams right now...looks like you live up to ur username
ye i did
Post by: khalil on August 28, 2009, 09:52:09 pm
Post by: Flaming_Arrow on August 28, 2009, 09:54:22 pm
So that means that Pr(B|A')Pr(A')=Pr(A n B')?
na
Pr(B|A')Pr(A')=Pr(B n A') \ Pr(A') * Pr(A') = Pr(B n A')
Post by: khalil on August 29, 2009, 12:31:17 pm
Does Pr(B')=Pr(A)?
Post by: khalil on August 29, 2009, 12:46:52 pm
bushwalking. One student from the school is chosen at random. Let G represent the event
that the student is a girl, and B represent the event that the student enjoys bushwalking.
Find Pr(G)....I dont know how to draw a tree diagram that will have an end branch of B and G
Post by: kamil9876 on August 29, 2009, 12:52:26 pm
Post by: shinny on August 29, 2009, 12:57:08 pm
At a certain school it was found that 35% of the 500 boys and 40% of the 400 girls enjoyed
bushwalking. One student from the school is chosen at random. Let G represent the event
that the student is a girl, and B represent the event that the student enjoys bushwalking.
Find Pr(G)....I dont know how to draw a tree diagram that will have an end branch of B and G
You can ignore B for this question. It's just asking the probability of finding a girl; nothing regarding whether they enjoy bushwalking or not. If there's 500 guys, 400 girls, using simple probability, the chance of choosing a girl is
Post by: khalil on August 29, 2009, 01:18:37 pm
At a certain school it was found that 35% of the 500 boys and 40% of the 400 girls enjoyed
bushwalking. One student from the school is chosen at random. Let G represent the event
that the student is a girl, and B represent the event that the student enjoys bushwalking.
Find Pr(G)....I dont know how to draw a tree diagram that will have an end branch of B and G
You can ignore B for this question. It's just asking the probability of finding a girl; nothing regarding whether they enjoy bushwalking or not. If there's 500 guys, 400 girls, using simple probability, the chance of choosing a girl is
lol. That was simple. Thanks
Post by: khalil on August 29, 2009, 01:21:53 pm
Does Pr(B')=Pr(A)?
Also, Pr(A|B)=Pr(B|A)?
Post by: shinny on August 29, 2009, 01:32:33 pm
Pr(A) = Pr(A|B) Pr(B) + Pr(A|B') Pr(B')
Draw up a Venn diagram and you'll get...
Does Pr(B')=Pr(A)?No, not in a general case. Venn diagram it and you'll see. Remember that there's things outside of both A and B.
Also, Pr(A|B)=Pr(B|A)?No.
But seriously, just go learn how to start using Venn diagrams and you can derive all of these yourself. You're not learning anything by asking us to prove every single one of these for you, as shown by your continual need to keep asking. Spend some time and learn how to do it yourself. I don't mind helping, but there's no point if you're not getting anything out of it.
Post by: khalil on August 29, 2009, 04:05:59 pm
Because isnt this how we get the law of probability? If not, someone please draw another tree diagram.
Post by: shinny on August 29, 2009, 04:15:47 pm
Post by: jaja on September 01, 2009, 08:42:26 pm
first you have to assign which is player is positive, ill take katia as positivei know it has been a long time but i forgot to ask...why does one have a negative value'?
so its 1 and -x
1 = Pr(1) + Pr(3) + Pr(5)
-x = Pr(0) + Pr(2) + Pr(4) or you can just do 1-(Pr(1) + Pr(3) + Pr(5))
now in order it to be fare mean must equal zero
so Pr(1) + Pr(3) + Pr(5) - x(Pr(0) + Pr(2) + Pr(4)) = 0
solve for x
Post by: Flaming_Arrow on September 01, 2009, 09:17:29 pm
first you have to assign which is player is positive, ill take katia as positivei know it has been a long time but i forgot to ask...why does one have a negative value'?
so its 1 and -x
1 = Pr(1) + Pr(3) + Pr(5)
-x = Pr(0) + Pr(2) + Pr(4) or you can just do 1-(Pr(1) + Pr(3) + Pr(5))
now in order it to be fare mean must equal zero
so Pr(1) + Pr(3) + Pr(5) - x(Pr(0) + Pr(2) + Pr(4)) = 0
solve for x
because its in terms of the players perspective, that is when one player loses money when another wins
Post by: khalil on September 01, 2009, 10:16:33 pm
first you have to assign which is player is positive, ill take katia as positivei know it has been a long time but i forgot to ask...why does one have a negative value'?
so its 1 and -x
1 = Pr(1) + Pr(3) + Pr(5)
-x = Pr(0) + Pr(2) + Pr(4) or you can just do 1-(Pr(1) + Pr(3) + Pr(5))
now in order it to be fare mean must equal zero
so Pr(1) + Pr(3) + Pr(5) - x(Pr(0) + Pr(2) + Pr(4)) = 0
solve for x
because its in terms of the players perspective, that is when one player loses money when another wins
I dont get it either! Please explain further!
Post by: Flaming_Arrow on September 01, 2009, 10:29:50 pm
first you have to assign which is player is positive, ill take katia as positivei know it has been a long time but i forgot to ask...why does one have a negative value'?
so its 1 and -x
1 = Pr(1) + Pr(3) + Pr(5)
-x = Pr(0) + Pr(2) + Pr(4) or you can just do 1-(Pr(1) + Pr(3) + Pr(5))
now in order it to be fare mean must equal zero
so Pr(1) + Pr(3) + Pr(5) - x(Pr(0) + Pr(2) + Pr(4)) = 0
solve for x
because its in terms of the players perspective, that is when one player loses money when another wins
I dont get it either! Please explain further!
ok just say i was playing a game with a friend where i win $1 if if its heads and he wins $1 if its tails, if he wins the game, i lose the the game i lose $1, which means -1
Post by: khalil on September 01, 2009, 10:33:38 pm
A newspaper seller buys papers for 50 cents and sells them for 75 cents, and cannot return
unsold papers.
If the newspaper seller stocks too many papers a loss is incurred. If too few papers are
stocked potential profit is lost because of the excess demand. Let s represent the number
of newspapers stocked, and X the daily demand.
a) If P is the newspaper seller’s profit for a particular stock level s, find and expression
for P in terms of s and X.
ans. 0.75x-0.5s x<s
0.5s-0.25x x>s
Post by: TrueTears on September 02, 2009, 07:12:49 pm
I remember asking about this question... if my memory serves me correct I think the answers were wrong...Ok I've confirmed the book having the wrong answers.
Post by: khalil on September 02, 2009, 08:21:25 pm
Post by: ngRISING on September 04, 2009, 11:08:37 pm
x/2√x . = ( x ) ( 2 x ^ -1/2 )
= [( x^2 )/2] x[( 2 x ^1/2 )/ .5]
= ???
a bit rusty. this question is taken from essetials 16C
Post by: d0minicz on September 04, 2009, 11:15:32 pm
=
=
=
Post by: ngRISING on September 04, 2009, 11:24:44 pm
Post by: Damo17 on September 04, 2009, 11:33:48 pm
why did x^1/2 move to the top. i know x^1/2 = squareroot x.
Post by: khalil on September 06, 2009, 04:16:23 pm
Say that the probability of something being accepted it 0.86 and prob of another thing being accepted is 0.77. They are not dependent.
To find the probability that they are both rejected, do we do this
(1-0.86)*(1-0.77) or this 1-(0.86*0.77)? The latter is correct, but why not the former?
Post by: Flaming_Arrow on September 06, 2009, 04:17:40 pm
Say that the probability of something being accepted it 0.86 and prob of another thing being accepted is 0.77. They are not dependent.
To find the probability that they are both rejected, do we do this
(1-0.86)*(1-0.77) or this 1-(0.86*0.77)? The latter is correct, but why not the former?
(1-0.86)*(1-0.77)
Post by: khalil on September 06, 2009, 04:26:33 pm
Say that the probability of something being accepted it 0.86 and prob of another thing being accepted is 0.77. They are not dependent.
To find the probability that they are both rejected, do we do this
(1-0.86)*(1-0.77) or this 1-(0.86*0.77)? The latter is correct, but why not the former?
(1-0.86)*(1-0.77)
?????
Post by: /0 on September 06, 2009, 04:29:54 pm
0.86*0.77 is the probability that both are accepted, so 1-(0.86*0.77) is the probability that NOT both of them are accepted, i.e. AT LEAST one is rejected.
(1-0.86)(1-0.77) is the probability that both are rejected.
Post by: shinny on September 06, 2009, 04:31:17 pm
Say that the probability of something being accepted it 0.86 and prob of another thing being accepted is 0.77. They are not dependent.
To find the probability that they are both rejected, do we do this
(1-0.86)*(1-0.77) or this 1-(0.86*0.77)? The latter is correct, but why not the former?
The first one represents the probability that both are rejected while the second represents the probability that not both are accepted. The difference is, the second one includes the cases where one is accepted, and the other not, whereas the first is specifically finding the probability of both being rejected.
EDIT: /0 beat me to it ]:
Post by: khalil on September 12, 2009, 04:02:14 pm
Each part costs $4 to produce; those that turn out too long are shortened at an extra cost of $2 and those that turn out to be too short have to be rejected. Find the exprected total cost of producing 100 parts that meet the requirements.
I did this: 96.2*4+0.03*4+0.008*6= 401.6....but the answers say 409.28
Post by: kamil9876 on September 12, 2009, 04:46:53 pm
The question is different, it wants how much you have to pay to be expected 100 GOOD parts. Let's say we need X parts in order to be expected to get 100 GOOD parts. Out of those X parts we expect
Hence we will pay 4X for the production and 2*0.03X for the shortening since 3% of them are too long.
That means altogether we pay"
4X+0.06X=4.06X=409.27$
Post by: khalil on September 12, 2009, 08:37:45 pm
Post by: khalil on September 13, 2009, 08:16:47 am
Post by: Mao on September 13, 2009, 08:55:47 am
It's something I picked up in specialist to rationalize surds:
Post by: khalil on September 13, 2009, 08:07:59 pm
Post by: kamil9876 on September 13, 2009, 08:33:10 pm
Post by: ngRISING on September 13, 2009, 10:16:49 pm
CH 17A . Q4c) ii].
Quesiton is . f(x) = [1/5√2pie]e^[(1/2)((x+4)/5)^2]
Find E(X^2) .
Post by: /0 on September 13, 2009, 10:27:02 pm
Then
However your calculator will probably have a hard time integrating this.
Instead note that the normal distribution is
So we have
So now we can say:
Post by: TrueTears on September 13, 2009, 10:29:10 pm
Post by: ngRISING on September 13, 2009, 10:35:25 pm
Post by: /0 on September 13, 2009, 10:39:07 pm
Or just use the NormalCDF if this was MC Q.
How would you use normCDF?
Post by: Gloamglozer on September 14, 2009, 06:21:47 pm
Or just use the NormalCDF if this was MC Q.
How would you use normCDF?
When it is a normal distribution and you need to add in a range of values.
EDIT: Actually, come to think of it, we never use normpdf, do we? So aren't we supposed to use normcdf if it a normal distribution?
Post by: /0 on September 14, 2009, 06:49:23 pm
Or just use the NormalCDF if this was MC Q.
How would you use normCDF?
When it is a normal distribution and you need to add in a range of values.
Yes but can you find expected values somehow?
Post by: TrueTears on September 14, 2009, 06:52:25 pm
Yeah normPDF gives the height of the density function. CDF gives the probability.Or just use the NormalCDF if this was MC Q.
How would you use normCDF?
When it is a normal distribution and you need to add in a range of values.
EDIT: Actually, come to think of it, we never use normpdf, do we? So aren't we supposed to use normcdf if it a normal distribution?
Post by: Gloamglozer on September 15, 2009, 07:23:25 pm
Yeah normPDF gives the height of the density function. CDF gives the probability.Or just use the NormalCDF if this was MC Q.
How would you use normCDF?
When it is a normal distribution and you need to add in a range of values.
EDIT: Actually, come to think of it, we never use normpdf, do we? So aren't we supposed to use normcdf if it a normal distribution?
When do we need to find the height of a density function? That's just the mode, right?
Post by: TrueTears on September 15, 2009, 09:00:48 pm
Yeah the mode is the X value that produces the height, not the actual height. Remember that XDYeah normPDF gives the height of the density function. CDF gives the probability.Or just use the NormalCDF if this was MC Q.
How would you use normCDF?
When it is a normal distribution and you need to add in a range of values.
EDIT: Actually, come to think of it, we never use normpdf, do we? So aren't we supposed to use normcdf if it a normal distribution?
When do we need to find the height of a density function? That's just the mode, right?
Post by: Gloamglozer on September 16, 2009, 04:38:26 pm
Post by: khalil on September 27, 2009, 09:59:30 pm
Post by: TrueTears on September 27, 2009, 10:06:45 pm
Post by: khalil on September 27, 2009, 10:09:03 pm
I can do it but I have to use the chain rule twice, first to derive g(x^2) then the whole thing
Post by: TrueTears on September 27, 2009, 10:09:40 pm
http://web.mit.edu/wwmath/calculus/differentiation/chain.html
Post by: khalil on September 27, 2009, 10:25:36 pm
Post by: TrueTears on September 27, 2009, 10:26:09 pm
Post by: khalil on September 27, 2009, 10:28:23 pm
Post by: TrueTears on September 27, 2009, 10:28:52 pm
Post by: QuantumJG on September 27, 2009, 10:37:42 pm
Why does 0! = 1?
Factorial (n!) is defined as the continued multiplication of 1...n (I.e. n! = 1*2*3*4*...*(n-2)*(n-1)*n, where n>0.
0! = 1, since, the product of no numbers is defined as equalling 1.
The only thing you need to know in maths methods is that 0! = 1. Even if that is required?
I hope in university I'll see how this is actually proved.
Post by: kamil9876 on September 27, 2009, 10:48:42 pm
Post by: ryley on September 27, 2009, 11:06:14 pm
(http://i33.tinypic.com/wbew5k.jpg)
Post by: khalil on September 29, 2009, 10:11:02 pm
Would this transformation be a dilation from the x or y axis.
Cos' when the graph is transformed it it 4/x
Post by: Flaming_Arrow on September 29, 2009, 10:16:03 pm
Post by: khalil on September 30, 2009, 12:42:00 am
Post by: TrueTears on September 30, 2009, 12:47:56 am
Let
Would this transformation be a dilation from the x or y axis.
Cos' when the graph is transformed it it 4/x
Thus the graph of
Thus
So this is a dilation of factor 4 from the y axis.
Post by: kamil9876 on September 30, 2009, 12:50:21 am
Post by: khalil on September 30, 2009, 08:52:56 am
Post by: kamil9876 on September 30, 2009, 12:27:47 pm
e.g:
y=x^2 to y=4x^2
could be seen as dilating 4 from x axis. However by expressing the second function as y=(2x)^2 you get dilation by factor of 1/2 from y axis. Different transformations that yield same result.
A more simple and intuitive example:
y=x to y=(x+2) could also be seen as y=x to (y-2)=x. This means that Moving the line y=x 2 units left has the same affect as moving the line y=x 2 units up(draw this to see yourself). Hence different transformations can give same result.
Post by: khalil on September 30, 2009, 05:01:48 pm
Post by: kamil9876 on September 30, 2009, 08:01:19 pm
a=4 is your case.
Post by: khalil on September 30, 2009, 10:50:02 pm
Post by: m@tty on September 30, 2009, 10:59:25 pm
Post by: khalil on September 30, 2009, 11:22:58 pm
There must be some sort of rule to draw these graphs
Post by: TrueTears on October 01, 2009, 04:23:46 pm
True, but how do I know that the y int of f(x) will be postive and not negativeYou won't know because the +c is vertical translation.
There must be some sort of rule to draw these graphs
Post by: khalil on October 03, 2009, 04:18:25 pm
Post by: ngRISING on October 04, 2009, 11:42:56 am
A) U = 100.4 . sd = 18.3
B) U = 111.3 . sd = 16.6
C) U = 69.2 . sd = 39.6
D) U = 110.8 . sd = 39.6
E) U = 98.7 . sd = 16.6
Post by: TrueTears on October 04, 2009, 03:54:10 pm
Let
Pr(X > 90) = 0.7
Pr(X > 120) = 0.1
Inverse normal of 0.7 = -0.5244
Inverse normal of 0.1 = 1.28155
Thus
Solve simultaneously.
Post by: khalil on October 04, 2009, 06:19:34 pm
Post by: TrueTears on October 04, 2009, 06:22:42 pm
What about my question :(Expected value is never to be rounded. It's the 'expected' value.
It's kind of like finding the average, say you have heaps of numbers eg, 1, 4, 7, 12, 15 and you want to find the average of those, the number you get will probably not be one of those numbers, but you still take it as the "average" that is similar to expected value, the value you "expect" doesn't have to make sense with the situation.
EDIT: sailor mars too fast =(
Post by: khalil on October 04, 2009, 06:25:10 pm
What about my question :(Expected value is never to be rounded. It's the 'expected' value.
It's kind of like finding the average, say you have heaps of numbers eg, 1, 4, 7, 12, 15 and you want to find the average of those, the number you get will probably not be one of those numbers, but you still take it as the "average" that is similar to expected value, the value you "expect" doesn't have to make sense with the situation.
EDIT: sailor mars too fast =(
thanks sailor moon!
Post by: VeryCrazyEdu. on October 04, 2009, 06:34:29 pm
Let X be the random variable for the weight and Z as the standard normal variable.
Let= s.d and
= mean
Pr(X > 90) = 0.7
When using inverses you have to make sure all the probabilities are Pr(X<__) otherwise it won't work. The inverse always measures the area from the left. so you should inverse Pr(X<90)=.3 etc.
i dunno if this is what you meant but hope i helped :)
Pr(X > 120) = 0.1
Inverse normal of 0.7 = -0.5244
Inverse normal of 0.1 = 1.28155
Thus
Solve simultaneously.
Post by: VeryCrazyEdu. on October 04, 2009, 06:36:35 pm
you have to make sure that all probabilities are in the form Pr(X<__) because inverse measures the area from the left.
Post by: TrueTears on October 04, 2009, 06:39:36 pm
lol sorry my reply didn't come up! hahaActually don't, from the calc it is always the upper right bound, so just take opposite sign of the answer from the calc because it's symmetrical about 0.
you have to make sure that all probabilities are in the form Pr(X<__) because inverse measures the area from the left.
Forgot to mention: only use symmetrical properties if it's the normal standard you are dealing with, if it is just normal distribution, you gonna have to do some arithmetic around the mean.
Post by: VeryCrazyEdu. on October 04, 2009, 06:43:41 pm
Post by: jaja on October 04, 2009, 10:22:27 pm
"the number of solutions to the equation (X^2 - a) (x^3 - b^3) (X + c)=0 where a,b,c is an element of R+....
the ans is 4.. however why????
when solving for x wouldn't X = plus or minus square root of a??? wouldn't we ignore the - since "a in an element of R+??? this goes the same for when X = -c
Post by: TrueTears on October 04, 2009, 10:25:39 pm
Insight 2008, Mc Q3)......
"the number of solutions to the equation (X^2 - a) (x^3 - b^3) (X + c)=0 where a,b,c is an element of R+....
the ans is 4.. however why????
when solving for x wouldn't X = plus or minus square root of a??? wouldn't we ignore the - since "a in an element of R+??? this goes the same for when X = -c
Total number of solutions: 4
Post by: ngRISING on October 04, 2009, 10:54:17 pm
Post by: TrueTears on October 04, 2009, 10:59:24 pm
Post by: ngRISING on October 04, 2009, 11:05:19 pm
Post by: TrueTears on October 04, 2009, 11:09:46 pm
Post by: ngRISING on October 04, 2009, 11:28:37 pm
Post by: jaja on October 04, 2009, 11:37:36 pm
Insight 2008, Mc Q3)......
"the number of solutions to the equation (X^2 - a) (x^3 - b^3) (X + c)=0 where a,b,c is an element of R+....
the ans is 4.. however why????
when solving for x wouldn't X = plus or minus square root of a??? wouldn't we ignore the - since "a in an element of R+??? this goes the same for when X = -cwould have 2 solutions.
which would have 1 solution.
would have 1 solution
Total number of solutions: 4
i get that part.. but the question states "where a,b,c are elements of R+.... All pOSITIVE REAl NUMBERS......
Post by: Mao on October 04, 2009, 11:46:37 pm
Hence, there are 4 roots as shown by TT.
Post by: jaja on October 05, 2009, 09:18:59 pm
Post by: jaja on October 05, 2009, 09:36:35 pm
also in VCCA sample exam 1, 2006; Q2a... when it asks to differentiate 3x^4 (times) tan(x)........would we lose marks if we just left it like.................3x^3 (4tanx + 3x/(cosx)^2)
6b)....find Pr (X<0.5)... since its a probability density function when finding the answer, can the answer be in units square, since its the area????
Q8c) if question states find "an- anti- derivative" does that mean C can be any value????
Post by: TonyHem on October 05, 2009, 11:35:25 pm
?http://vcenotes.com/forum/index.php/topic,17530.0.html
Q8c) if question states find "an- anti- derivative" does that mean C can be any value????
and for the derivative question, you made a mistake but that form is fine unless you mean whether you have to fully simplify - which is most likely unless its like a 1 mark q.
Post by: dcc on October 05, 2009, 11:45:00 pm
6b)....find Pr (X<0.5)... since its a probability density function when finding the answer, can the answer be in units square, since its the area????
I don't have the question your asking, but if it's asking for a probability, it just means a unitless number in between 0 and 1 (inclusive). While the concept of 'area under the curve' is useful for understanding some of the properties of integrals, it doesn't always work the other way (i.e. an integral isn't necessarily an area) :P
Post by: jaja on October 06, 2009, 12:49:37 am
Post by: jaja on October 06, 2009, 01:09:16 am
2007 VCCA exam 1........Q11)... can i just leave than answer as (0.4 * 0.8) + (0.6 * 0.6)... or would i need to multiply and then add the decimals??? if i
just leave it like that would i still get the full 2 marks???
Q8b)... how do you get 7/4.. .didn't understand VCCA's answer
Post by: TonyHem on October 06, 2009, 01:43:03 am
Post by: khalil on October 07, 2009, 11:08:31 am
Post by: khalil on October 07, 2009, 11:20:19 am
Post by: Flaming_Arrow on October 07, 2009, 01:41:54 pm
For this question, if I just wrote: cos^-1(y), y cannot take values greater than 1, would this suffice?
when
Post by: Flaming_Arrow on October 07, 2009, 01:42:30 pm
Also, do they mean a<0 in this question or am I just drunk?
yes a<0
Post by: khalil on October 09, 2009, 09:27:18 pm
Post by: kurrymuncher on October 09, 2009, 09:28:26 pm
quick question: if question says dilate from y axis, does that mean the x values change or the y values?
X values
Post by: khalil on October 09, 2009, 09:31:55 pm
Post by: kurrymuncher on October 09, 2009, 09:32:27 pm
Post by: khalil on October 09, 2009, 09:36:32 pm
Post by: kurrymuncher on October 09, 2009, 09:39:10 pm
Then is there a mistake in the insight exam 1 2006 Q2)c)...please check
lols maybe Im just wrong, I had too many trial exams in the past three days :buck2:
wait for TT
Post by: TrueTears on October 09, 2009, 10:01:24 pm
srry, I meant 'along'Along y axis just means dilate FROM the x axis, so the y values will change. kurrymuncher is right :) pr0 pr0
Post by: khalil on October 09, 2009, 10:27:04 pm
Post by: TrueTears on October 09, 2009, 10:32:42 pm
Dilation factor of
Post by: khalil on October 09, 2009, 10:36:24 pm
Post by: TrueTears on October 09, 2009, 11:03:44 pm
In orther words, the answer given is wrong?Yeah.
Post by: ngRISING on October 12, 2009, 01:06:27 am
In orther words, the answer given is wrong?Yeah.
phew. just did it lol. thought i got it wrong as well. didnt do too well on this prac exam. 75% :S .
Post by: TrueTears on October 12, 2009, 01:11:59 am
I'm sure you will improve, just do more exams :PIn orther words, the answer given is wrong?Yeah.
phew. just did it lol. thought i got it wrong as well. didnt do too well on this prac exam. 75% :S .
Good luck :)
Post by: khalil on October 12, 2009, 08:45:10 pm
Post by: Gloamglozer on October 13, 2009, 04:22:25 pm
TSFX sent this, and they don't mention how to do it correctly to lure us to their lectures...can someone explain
Went to their lectures on the holidays and my lecturer didn't mention it.
Post by: khalil on October 13, 2009, 04:32:23 pm
Post by: Gloamglozer on October 13, 2009, 04:42:37 pm
Post by: GerrySly on October 13, 2009, 04:44:13 pm
Does anyone know the difference between solve and nSolve?nSolve gives numeric answers and solve gives exact answers. I think nSolve is faster being it doesn't have to rationalise or anything like that
Post by: khalil on October 13, 2009, 04:48:39 pm
Post by: khalil on October 13, 2009, 05:19:48 pm
I've spent so long trying to figure this out
Post by: TrueTears on October 13, 2009, 05:22:54 pm
I use 2ND + <- for TI-83
Post by: khalil on October 13, 2009, 05:49:27 pm
Post by: jaja on October 14, 2009, 07:19:17 pm
If a panel of two people is selected at random from the population, 60% of whom are aged 25 years or less, find:
the probability that the panel contains the same number of people aged 25 years or less and people aged over 25 years
Post by: bigtick on October 14, 2009, 08:25:45 pm
Post by: khalil on October 15, 2009, 09:33:07 am
Post by: ngRISING on October 18, 2009, 09:26:05 pm
Question 19
The probability of Kimmy getting a maths question correct in a test is 0.24. What is the fewest number of questions the maths teacher should set to ensure that the probability of Kimmy getting at least two questions correct is more than 0.95?
A. 18
B. 17
C. 16
D. 15
E. 14
Question 2
Which of the following is the definition of an odd function?
A. f(-x) = - f(x)
B. f(x) = f(-x)
C. f(x) = xn, where n is odd
D. f(x) = - f(0)
E. f(x) = -x
Question 14
The remainder when the function f(x) = x5 - 4x4 + 3x3 + 2x + 1 is multiplied by is:
A. 0
B. 9
C. 24
D. -3
E. -32
Question 15
2000 metres up in the air, a plane is flying horizontally at a constant speed. At a particularly point in time, the angle is 30◦ and decreasing, and the speed of the aeroplane is 450 km/h. How quickly is the angle decreasing at this point?
A. – 0.013 degrees per hour
B. 0.23 degrees per hour
C. -0.23 degrees per hour
D. 0.11 degrees per hour
E. 0.0140 degrees per hour
Post by: TrueTears on October 18, 2009, 09:27:58 pm
Anyway
Q2. A, the definition of a odd function is that a reflection in the x axis is the same as a reflection in the y axis.
Post by: ngRISING on October 18, 2009, 10:17:02 pm
lol is that from the Medtutor exam?
Anyway
Q2. A, the definition of a odd function is that a reflection in the x axis is the same as a reflection in the y axis.
yup. i kinda dislike this exam for some reason. maybe i screwed up a lot of the questions LOL .
Post by: TonyHem on October 19, 2009, 12:47:09 am
N = unknown
X = at least 2
1 - binomCDF(n,0.24,1) - you can just do trial and error here.
or
1- nc0(0.24)^(0)*(0.76)^n + nc1(0.24)(0.76)^(n-1) > 0.95
1 - (0.76^(n) + n(0.24)(0.76)^(n-1) > 0.95
0.76^(n) + 0.24n(0.76)^(n-1) < 0.05 or <-- this may be easier
I dunno how to actually "solve it" properly :/
Post by: ngRISING on October 25, 2009, 12:45:20 pm
tech free 09
sketch the graph wit equation f(x) = -(x-4)(x+2)^2(1-x)^5 labelling the coordinates of the axes intercepts.
how the f*** would i sketch that without a calc ?
Post by: Flaming_Arrow on October 25, 2009, 12:51:06 pm
TSFX.
tech free 09
sketch the graph wit equation f(x) = -(x-4)(x+2)^2(1-x)^5 labelling the coordinates of the axes intercepts.
how the f*** would i sketch that without a calc ?
well its in factor form so just sketch the interceps and sub in random values of x(0,1,-1) etc to sektch it
Post by: TrueTears on October 25, 2009, 03:01:34 pm
Looking at the highest power of x which is x^8, it is an even power so it will look like the "even" power graphs.
You will have a x axis intercept at x = 4 and x = -2 and one at x = 1
However lets take a look at the furthest to the right x intercept. Since f(x) is "positive" that means it comes down from the positive half of the y axis. So it comes down from the first quadrant going into the fourth.
At
Then at
Post by: ngRISING on October 29, 2009, 10:25:10 pm
say e^x = x
for my next line do i need to put
loge (e^x) = loge(x)
or can i just put
x = loge(x)
ty
Post by: /0 on October 29, 2009, 10:29:10 pm
Post by: ngRISING on October 29, 2009, 10:40:04 pm
Post by: ngRISING on October 29, 2009, 10:43:01 pm
say the q was
0=4cos(pie/x)-2
can i just write
1/2=cos(pie/x) for the next line
methods might actually be fun for me now LOL
Post by: TonyHem on October 29, 2009, 11:01:26 pm
edit: no sorry, you can't write pie or pi, you must write
hehe
Post by: ngRISING on October 29, 2009, 11:10:05 pm
Post by: ngRISING on October 29, 2009, 11:18:29 pm
heres the question cause i dont understand the theory
(http://img215.imageshack.us/img215/3295/mav08.jpg)
part b
u know when it says f(2x) which i misread has 2(f(X))
if it was f(2x) it would be
2cos[2(pie/x)]-1
if it was 2(f(x)) it would be
2[2cos(pie/x)-1]
right. hence it explains my earlier question lol ==' .
Post by: TonyHem on October 29, 2009, 11:27:31 pm
Post by: ngRISING on October 29, 2009, 11:32:22 pm
Post by: TonyHem on October 29, 2009, 11:36:47 pm
part b
if it was f(2x) it would be
2cos[2(pie/x)]-1 ( I mean here, you have pi/x, but the equation is, so wouldn't changing x for 2x just give you
)
if it was 2(f(x)) it would be
2[2cos(pie/x)-1]
Post by: ngRISING on October 29, 2009, 11:54:24 pm