Bounds for the mean of the minimum of binomial random variables

AI Thread Summary
The discussion focuses on finding upper and lower bounds for the expected value of the minimum of independent binomial random variables. The original poster seeks recommendations for papers or books addressing this problem, emphasizing the difficulty in evaluating the minimum theoretically due to the lack of a closed formula for the cumulative distribution function (CDF) of the binomial distribution. Participants suggest considering existing expressions, such as the floor-sum expression for the CDF. The challenge lies in deriving bounds instead of directly computing the expected value. Overall, the conversation highlights the complexities involved in statistical analysis of binomial distributions.
soroush1358
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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.
 
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Why do you need bounds, have you thought of deriving/computing the expected value directly?
 
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.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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