Let X be a continuous random variable with density function be-bx for a > 0 otherwise , f(x) = where b> 0. - find M(t) the moment generating function of X, then what is E(x) ?

Suppose you have two independent random variables X ~ Y ~ Exponential(A2), A1 > 0, d2 > 0. Find: Exponential(A1) and (a) The joint density function for (X,Y). (b) P( > 1). (c) P(X +Y > 1).

Suppose that X and X, have joint probability density function x2, if 1< xı < 2 and 1 < r2 < 3 10, fx1.x.("1, 2) = otherwise. What is the joint probability density function fy,y, of Y1 = X1/X2 and Y, = X2?

Example of (a) , (b) is (12),(24),(1),(6) Example of (c) (i) or (ii)   Thanks