6. Let (X,Y) have the following joint density function: 12y? 0

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6. Let (X,Y) have the following joint density function:
12y? 0<y <x <1
f(x, y)
otherwise
a. Find the marginal distribution of Y, f(y).
b. Find the conditional distribution of X given Y=y, f(x|y).
c. Find E(X|Y=y), the expectation of X given Y=y.
Transcribed Image Text:6. Let (X,Y) have the following joint density function: 12y? 0<y <x <1 f(x, y) otherwise a. Find the marginal distribution of Y, f(y). b. Find the conditional distribution of X given Y=y, f(x|y). c. Find E(X|Y=y), the expectation of X given Y=y.
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