Suppose that X and Y are continuous with joint PDF {0(₁- [c(1-y) for 0 2/3. (c) Find the expected value of X. (d) Find the expected value of Y.

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Suppose that X and Y are continuous with joint PDF
f(x,y)
=
[c(1-y) for 0<x<y<1
0
otherwise
where c is a yet-to-be-determined constant.
(a) Find the value of c that makes this a valid joint PDF.
(b) Calculate the probability that X < 1/2 when Y > 2/3.
(c) Find the expected value of X.
(d) Find the expected value of Y.
Transcribed Image Text:Suppose that X and Y are continuous with joint PDF f(x,y) = [c(1-y) for 0<x<y<1 0 otherwise where c is a yet-to-be-determined constant. (a) Find the value of c that makes this a valid joint PDF. (b) Calculate the probability that X < 1/2 when Y > 2/3. (c) Find the expected value of X. (d) Find the expected value of Y.
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