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  • https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_ASCCC/Statistics%3A_UC_Davis/1%3A_Notes/1.08%3A_08_Special_distributions_and_their_properties
    \hspace{-120.0pt} \begin{tabular}{|l|l|lc|c|c|c|} \hline Name & Notation & Formula & & \(\textbf{E}(X)\) & \(\textbf{V}(X)\) & \(\textbf{E}(X^k)\) \\ \hline Discrete uniform & \(X\sim U\{1,\ldots,n\}\...\hspace{-120.0pt} \begin{tabular}{|l|l|lc|c|c|c|} \hline Name & Notation & Formula & & \(\textbf{E}(X)\) & \(\textbf{V}(X)\) & \(\textbf{E}(X^k)\) \\ \hline Discrete uniform & \(X\sim U\{1,\ldots,n\}\) & \(\prob(X=k) = \frac{1}{n}\) & \((1\le k\le n)\) & $\frac{n+1}{2}$ & \(\frac{n^2-1}{12}\) & \\ Bernoulli & \(X\sim \textrm{Bernoulli}(p)\) & \(\prob(X=0)=1-p,\ \prob(X=1)=p$ & & \(p\) & \(p(1-p)\) & \(p\) \\ Binomial & \(X\sim \textrm{Binomial}(n,p)\) & \(\prob(X=k)=\binom{n}{k}p^k (1-p)^{n-k}\…

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