Let X and Y be independent exponential random variables with respective rates and . Find (a)

Let X and Y be independent exponential random variables with respective rates λ and μ. Find

(a) Cov(X, min(X, Y))

(b) Cov(X,max(X, Y))

(c) Cov(min(X, Y),max(X,Y))

(d) Find P(X <2Y).