Question: I need these solutions. Assignment 6 1. Let X and Y have joint pdf: fX,Y (x, y) = k(x + y) for 0 x 1,

I need these solutions.

Assignment 6 1. Let X and Y have joint pdf: fX,Y (x, y) = k(x + y) for 0 x 1, 0 y 1. (a) Find k. (b) Find the joint cdf of (X,Y). (c) Find the marginal pdf of X and of Y . (d) Find P [X 0.5]. 2. The random vector (X, Y ) is uniformly distributed (i.e., f (x, y) = k) in the regions shown in the following figures and zero elsewhere. (i ) (iii ) (ii ) 1 1 1 1 1 1 (a) Find the value of k in each case. (b) Find the marginal pdf for X and for Y in each case. (c) Find P [X > 0, Y > 0]. 3. Let X and Y be independent random variable. Find the expression for the probability of the following events in terms of FX (x) and FY (y). (a) {a d}. (b) {a

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