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Suppose the random variable (X, Y ) has a joint pdf for the form ?cxy 0≤x≤1,0≤y≤1...

Suppose the random variable (X, Y ) has a joint pdf for the form

?cxy 0≤x≤1,0≤y≤1 f(x,y) = .

0 elsewhere

  1. (a) (5 pts) Find c so that f is a valid distribution.

  2. (b) (6 pts) Find the marginal distribution, g(x) for X and the marginal distribution for Y , h(y).

  3. (c) (6 pts) Find P (X > Y ).

  4. (d) (6 pts) Find the pdf of X +Y.

  5. (e) (6 pts) Find P (Y < 1/2|X > 1/2).

  6. (f) (6 pts) Find E(X + Y ).

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