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# cheatsheet - Useful formulas If X is a binomial random...

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Useful formulas If X is a binomial random variable with parameters n and p , then p X ( k ) = ± n k ² p k (1 - p ) n - k , k = 0 , 1 ,...,n . E ( X ) = np, Var( X ) = np (1 - p ). If X is a negative binomial random variable with parameters n and p , then p X ( k ) = ± k - 1 n - 1 ² p n (1 - p ) k - n , k = n,n + 1 ,... E ( X ) = n/p, Var( X ) = n (1 - p ) /p 2 . If X is a hypergeometric random variable with parameters n,N and M , then p X ( k ) = ( N k )( M n - k ) ( N + M n ) , max( n - M, 0) k min( n,N ). E ( X ) = nN N + M , Var( X ) = nNM ( N + M ) 2 ± 1 - n - 1 N + M - 1 ² . If X is a Poisson random variable with parameter λ > 0, then p X ( k ) = λ k k ! e - λ , k = 0 , 1 , 2 ,... E ( X ) = Var( X ) = λ . If X is a uniform random variable taking values in ( a,b ), then f X ( x ) = 1 b - a , a < x < b . E ( X ) = a + b 2 , Var( X ) = ( b - a ) 2 12 . If X is a beta random variable with parameters α > 0 and β > 0, then f X ( x ) = 1 B ( α,β ) x α -

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cheatsheet - Useful formulas If X is a binomial random...

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