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

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

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

Transcribed Image Text:

E[min(X, Y)|X>Y+c]=E[min(X, Y)|X > Y] =E[min(X, Y)] = 1 2+