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The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.
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Calculate $E[X]^2$ where $X \sim \operatorname{Binomial}(n,p)$ with binomial coefficients ex... [closed]
Calculation of $EX$ using the binomial expansion formula is easy:
\begin{align}
EX &= \sum_{x=0}^{n}x\frac{n!}{(n-x)!x!}p^{x}(1-p)^{n-x}\\& = np \sum_{x=1}^{n}\frac{(n-1)!}{(n-x)!(x-1)!}p^{x-1}(1-p)^ …