Birth and death process

Prob. 1. Let X and Y be statistically independent random variables with uniform distribution on [-2, 2] and [-1, I]. respectively. (a) Sketch the probability density functions, Jy (x) and f(y)- (b) Let Z - X - Y. Sketch the probability density function, f (=). (c) Obtain P[Z 21]. (d) Obtain E[Z]. (c) Obtain of- Prob. 2. Any point (X, Y) in the shaded area below is selected equally likely. (a) Determine the joint probability density function fry (x.y). Clearly state the domain of the joint density function. (b) Sketch the probability density function /, (x). (c) Sketch the probability density function f,(y). (d) Are X and Y independent? (e) Obtain P (-0.5