Question

Let $X$ and $Y$ be independent non negative integer valued random variables with $E(X) < \infty$, $E(Y) < \infty$, then

• A. $E(\min(X, Y)) = \sum_{R=0}^{\infty} P(XY > R)$
• B. $E(\min(X, Y)) = \sum_{R=0}^{\infty} P(X \le R)P(Y \le R)$
• C. $E(\min(X, Y)) = \sum_{R=0}^{\infty} P(X > R) \cdot P(Y > R)$
• D. $E(\min(X, Y)) = \sum_{R=0}^{\infty} P(X Y \le R)$

Hint:

The discrete version of the survival function expectation rule is $\sum P(X > n)$, while the continuous version is $\int P(X > x) dx$. They are equivalent representations of the same fundamental concept.

Answer 1

The Correct Option is C