Let X and Y be independent exponential random variables with respective rates and . (a) Argue
Question:
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 ]
= E[min(X, Y )] =
1
λ + μ
(c) Give a verbal explanation of why min(X, Y ) and X −Y are (unconditionally)
independent.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: