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A joint density function is given by fX,Y (x, y) = ( kx, 0 < x...

A joint density function is given by fX,Y (x, y) = ( kx, 0 < x < 1, 0 < y < 1 0, otherwise.

(a) Calculate k

(b) Calculate marginal density function fX(x)

(c) Calculate marginal density function fY (y)

(d) Compute P(X < 0.5, Y < 0.1)

(e) Compute P(X < Y )

(f) Compute P(X < Y |X < 0.5)

(g) Are X and Y independent random variables? Show your reasoning (no credit for yes/no answer).

(h) Calculate Cov(X, Y )

Math   Statistics-And-Probability   
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