VCE Methods Question Thread!

[Adiamond]

Can anyone please check my working out and answer for this question?

Thanks 

Looks fine to me.

[teganlongworth]

Please help me with this continuous random probability question! SEE PICTURE ATTACHED! Thankyou

[warya]

Please help me with this continuous random probability question! SEE PICTURE ATTACHED! Thankyou

Cas assisted right? Define as a hybrid function on your calculator then antidiff x*g(x) within the specified domain for the mean.

[odeaa]

Consider the family of functions where and is a real constant and .

For any one set of graphs of and , how many possible solutions are there to ?

Have never seen the subscript notation before. From MAV Exam 2 2012

[Orb]

Consider the family of functions where and is a real constant and .

For any one set of graphs of and , how many possible solutions are there to ?

Have never seen the subscript notation before. From MAV Exam 2 2012

Just the same thing as f(x) i believe

[qwerty101]

help on this one please,

ans: 0.04

[qwerty101]

Also confused with this one. to find median

i know that median is the value at which the area of the pdf =1/2, however in their solution they have found medium using the 2nd equation where x is between 5 and 15 to find the median.

I would've thought that you find the area under the first equation which is 1/3 then gone

1/3 + (what they did in solution) = 1/2 , so it takes into account the whole pdf? thanks

[qwerty101]

sorry for the questions, also this one.

Why between 0 and 11, and say not 15 and 4 ?

thanks

[StupidProdigy]

Also confused with this one. to find median

i know that median is the value at which the area of the pdf =1/2, however in their solution they have found medium using the 2nd equation where x is between 5 and 15 to find the median.

I would've thought that you find the area under the first equation which is 1/3 then gone

1/3 + (what they did in solution) = 1/2 , so it takes into account the whole pdf? thanks

Yes that's right. You need to consider the area of the first part of the hybrid which usually is <1/2 in these types of questions and then set the second hybrid integral equal to 1/2-first integral value

[qwerty101]

thanks for that!!

im still stuck on the one with pr (0 < x < 11) and the question about the cards!

thanks

[qwerty101]

wondering why Pr(a) = Pr(b) ?

since pr(a intersect b) does not necessarily equal pr (b intersect a) therefore they cant really cancel each other out.

[keltingmeith]

wondering why Pr(a) = Pr(b) ?

since pr(a intersect b) does not necessarily equal pr (b intersect a) therefore they cant really cancel each other out.

No... They're equal. I suggest shading in the area on a venn diagram for further re-enforcement.

[qwerty101]

No... They're equal. I suggest shading in the area on a venn diagram for further re-enforcement.

yeah that was pretty stupid on my behalf haha i get ya, dont know why i said that lol.

[Orson]

How would you do this tech free? I don't see how the domain and range of f(x) are both [1, infinity)

Let f(x) = loge(x) and g(x) = x^2 + 1. Both functions have a maximal domain. Find the range of the function h = f(g(x))

Are these rules true?
dom h = ran f, ran h = dom f

Thanks!

[keltingmeith]

How would you do this tech free? I don't see how the domain and range of f(x) are both [1, infinity)

Let f(x) = loge(x) and g(x) = x^2 + 1. Both functions have a maximal domain. Find the range of the function h = f(g(x))

Are these rules true?
dom h = ran f, ran h = dom f

Thanks!

Nope - the domain of h is the domain of g. The range is a bit more interesting, see if you can find a way to determine it (hint: it is related to the range of f)