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

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

(a) Argue that, conditional on , the random variables and are independent.

(b) Use part

(a) to conclude that for any positive constant c

(c) Give a verbal explanation of why and are (unconditionally) independent.

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