Question

Consider the joint density function f (x, y) = 1 if 0<= x<= 1; 0<=y<= 1....

Consider the joint density function f (x, y) = 1 if 0<= x<= 1; 0<=y<= 1. [0 elsewhere]
a) Obtain the probability density function of the v.a Z, where Z = X^2.
b) Obtain the probability density function of v.a W, where W = X*Y^2.
c) Obtain the joint density function of Z and W, that is, g (Z, W)

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Answer #1

i had a confusion regarding W as you wrote W=X*Y^2 so i had a doubt between (X*Y)^2 and X*(Y^2) so i chose the latter

hence the solution for the last two parts are by taking W=X*(Y^2)...if this is not the case do comment below and i can change solution accordingly...below 2 images have the solution...so check them out!!

image 1:

image 2:

cheers :)

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