# Bounds for the mean of the minimum of binomial random variables

1. Jun 15, 2010

### soroush1358

Dear Friends,
I want to find an upper and lower bound for the expected value of the minimum of independent binomial random variables. What paper/book do you suggest for this problem?

In other words, I need to find bounds for E(min(X1,X2,...,Xn)), where Xi 's are independent random variables with binomial distribution.

2. Jun 15, 2010

### EnumaElish

Why do you need bounds, have you thought of deriving/computing the expected value directly?

3. Jun 16, 2010

### soroush1358

There is not any close formula for the cdf of binomial distribution. Hence, it seems that the minimum can not be evaluated theoretically. As a result of this, I prefer to find some upper and lower bounds for it.

4. Jun 17, 2010