3. Let (X, Y) have joint density function 4x f(x, y) + y?, 0

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3. Let (X, Y) have joint density function
4x
f (x, y)
+ y², 0<x < 1, 0 < y < 1.
3
(a) Find the marginal pdfs of X and Y.
(b) Compute P(X < 0.5) and P(0.2 <Y < 0.8)
(c) Compute E(X +Y).
(d) Compute Var (X) and Var(Y).
Transcribed Image Text:3. Let (X, Y) have joint density function 4x f (x, y) + y², 0<x < 1, 0 < y < 1. 3 (a) Find the marginal pdfs of X and Y. (b) Compute P(X < 0.5) and P(0.2 <Y < 0.8) (c) Compute E(X +Y). (d) Compute Var (X) and Var(Y).
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