VCE Methods Question Thread!

[TrueTears]

TWO bowls each contain 10 pieces of fruit. In a pink bowl there are 5 oranges and 5 bananas, in the the purple bowl there is one orange and 9 bananas,


for each bowl, find the prob that two pieces of fruit chosen at random will both be bananas, if the first piece is not replaced before the second piece of fruit is chosen???


AND one bowl is chosen at random and from it one piece of fruit is chosen at a random, Find the prob. that the piece of fruit chosen is a banana?

Consider the pink bowl, clearly drawing the type of fruit follows a hypergeometric distribution. http://en.wikipedia.org/wiki/Hypergeometric_distribution#Definition

The purple bowl also follows a hypergeometric distribution.

Now all you have to do is plug in the numbers

[catwoman101]

TWO bowls each contain 10 pieces of fruit. In a pink bowl there are 5 oranges and 5 bananas, in the the purple bowl there is one orange and 9 bananas,


for each bowl, find the prob that two pieces of fruit chosen at random will both be bananas, if the first piece is not replaced before the second piece of fruit is chosen???


AND one bowl is chosen at random and from it one piece of fruit is chosen at a random, Find the prob. that the piece of fruit chosen is a banana?

Consider the pink bowl, clearly drawing the type of fruit follows a hypergeometric distribution. http://en.wikipedia.org/wiki/Hypergeometric_distribution#Definition

The purple bowl also follows a hypergeometric distribution.

Now all you have to do is plug in the numbers

im sorry could i have some more help
?

[BubbleWrapMan]

For the pink bowl, the probability of the first fruit chosen being a banana is 5/10 = 1/2. After that there are 4 bananas and 5 oranges left. So, the probability of the second fruit chosen being a banana is 4/9. Multiplying those probabilities together gives 2/9, which is the probability that two fruit chosen at random from the pink bowl are both bananas.

Using a similar approach for the purple bowl, the probability is 9/10 * 8/9 = 4/5

Now for the next part, we can assume that each bowl has an equal chance of being chosen, i.e. the probability of choosing either bowl is 1/2

The probability of choosing a banana from the pink bowl is 1/2 * 1/2 = 1/4

The probability of choosing a banana from the purple bowl is 1/2 * 9/10 = 9/20

These two situations are disjoint, so the final probability is the sum of those two, which is 7/10

[Jenny_2108]

One can actually show that the maximum likelihood estimator of the parameter p in a binomial distribution is always given by , this is derived as follows:

Assume we have a sample of X_i's which are identically and independently distributed binomial random variables.

The pmf is thus given by , we now construct what is known as the likelihood function which is a function of the parameter p in this case:

Now if we take logs on each other we get:



Now if we take the first order derivative with respect to p:



Set this to 0 and solve for p yields:

as required.

Nice 

Btw TT, I let and solve for p but didn't get

Where did I do wrong?
















But


Therefore


How can I prove (1)=(2)? Did I do somewhere wrong? 

And what does this notation mean?

[pi]

Ennjy is the new TT

im sorry could i have some more help
?

Hypergeometrics were on the old Methods Course, ignore those qs from prac exams

[hongs-]

Hi guys I just wanted to asked a quick question on the VCAA Exam 2 2009 one
for Questions 2a ii. it says hence show that a=1 , b=-6 and c=16

You can use CAS since its an exam 2 but would i have to work out how i get a,b,c by hand ? i cant just write solve (_____,a,b,c) can i??
I should be solving it simultaneously by hand for full marks right?

[hongs-]

Also, how would you calculate qn2biii on VCAA 2009 exam 2?

The maximum depth of the valley, is that to do with derivatives...

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009mmCAS2-w.pdf

[Jenny_2108]

Hi guys I just wanted to asked a quick question on the VCAA Exam 2 2009 one
for Questions 2a ii. it says hence show that a=1 , b=-6 and c=16

You can use CAS since its an exam 2 but would i have to work out how i get a,b,c by hand ? i cant just write solve (_____,a,b,c) can i??
I should be solving it simultaneously by hand for full marks right?

yeah, you can use CAS but I just do by hand
You substitute them separately
From ai) 6a+b=0 => b=-6a
Sub into 3a+b=-3 to find a=1, thus b=-6
Sub a=1, b=-6 into 8a+4b+c=0 => c=16

Also, how would you calculate qn2biii on VCAA 2009 exam 2?

The maximum depth of the valley, is that to do with derivatives...

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009mmCAS2-w.pdf

I sub x=4 into y=
y=

Thus, the max depth is

[Homer]

A cubic function has the rule y=f(x). The graph of the derivative function crosses the x-axis at (2.0) and (-3,0). The maximum value of the derivative function is 10. The value of x for which the graph of y=f(x) has a local maximum is ___________?

[Jenny_2108]

A cubic function has the rule y=f(x). The graph of the derivative function crosses the x-axis at (2.0) and (-3,0). The maximum value of the derivative function is 10. The value of x for which the graph of y=f(x) has a local maximum is ___________?

(2,0)

[Homer]

why not (-3,0) and also I don't understand Question 3g 2009 Exam 2.

[Hutchoo]

is the same as , but instead of addition, it's multiplication.
E.g

=

[soccerboi]

Consider the graph y=x³. If a question asks for the domain in which the graph is an increasing function, would x=0 be included?

[Jenny_2108]

why not (-3,0) and also I don't understand Question 3g 2009 Exam 2.

Draw the graph of derivative function and you will see f'(x) change from negative to positive value at (-3,0)

Q3g) I use matrix, dunno how to type Latex though
I use transition matrix (T^n) and try trials, errors to find n

is the same as , but instead of addition, it's multiplication.
E.g

=

Thanks heaps Hutchoo

Consider the graph y=x³. If a question asks for the domain in which the graph is an increasing function, would x=0 be included?

included

[D.H]

Consider the graph y=x³. If a question asks for the domain in which the graph is an increasing function, would x=0 be included?

included

I was under the impression that strictly increasing means including x=0 but just increasing does not include x=0.
Can anyone else confirm?