Bounds for the mean of the minimum of binomial random variables

[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.

Thanks in advance.

 

[EnumaElish]

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

 

[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.

 

[EnumaElish]

There is not any close formula for the cdf of binomial distribution.

You mean, other than this floor-sum expression: http://en.wikipedia.org/wiki/Binomial_distribution#Cumulative_distribution_function ?