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

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

and μ.

(a) Argue that, conditional on X >Y, the random variables min(X, Y) and X−Y are independent.

(b) Use part

(a) to conclude that for any positive constant c E[min(X,Y)|X > Y + c] = E[min(X, Y)|X > Y]

(c) Give a verbal explanation of why min(X,Y) and X −Y are (unconditionally)
independent.

Transcribed Image Text:

= E[min(X, Y)] = 1