Re: Minimimum of N discrete RV
- From: "Stephen J. Herschkorn" <sjherschko@xxxxxxxxxxxx>
- Date: Fri, 27 Jan 2006 22:41:45 -0500
Intiha wrote:
whats the best way to find atleas the expectation of the minimum of N discrete uniformly distributed RV? Discrete is important since in the continuous case I would take the 1st order statistic and get its expectation.
If X is a natural-number-valued random variable (commonly called nonnegative discrete), then EX = sum(k=1..infty, P{X >= k}). Hence, if X is the minimum of n i.i.d. natural-valued r.v.'s Y1, Y2, ..., Y_n, then EX = sum(k=1..infty, P{Y1 >= k}^n). If your N is itself a random variable, condition thereon.
If your discrete random variables take on values other than natural numbers, then you have to modify this approach. In general, for any nonnegative random variable X, EX = integral(u=0..infty, P{X > u}).
-- Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx Math Tutor on the Internet and in Central New Jersey and Manhattan
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