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#1 2016-05-11 21:23:34

derek112
Guest

mathematical stats question

Consider two rvs X and Y with joint pdf f(x,y)=k-y, 0<y<x^2<1 .
(a) Sketch the region in two dimensions where f(x,y) is positive.Then find the constant k and sketch f(x,y) in three dimensions.
(b) Find and sketch the marginal pdf f(x), the conditional pdf f(x|1/2),and the conditional cdf F(y|1/2).
(c) Find P(x<Y|Y >1/2), E(X|Y=1/2)  and E(X|Y>1/2)
(d) What is the correlation between X and Y?
Are X and Y independent? Justify your answer.
(e) Find the value of the pdf of U = X + Y evaluated at u=0.8.
Hence, or otherwise, estimate P(0.8<x+y<0.801)

#2 2016-05-12 04:20:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: mathematical stats question

Hi;

If you would show some of your work then we could see where you need help.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-05-13 19:22:03

kkkrist112
Member
Registered: 2016-05-13
Posts: 1

Re: mathematical stats question

well, for part a i got this
∫∫k-ydydx=1 -1<x<1, 0<y<x^2
then i solved for k=9/5

for part b, i have trouble working out the f(x|1/2) and F(y|1/2), because i don't how to get marginal pdf f(y)

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