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352FormulaSheet

# 352FormulaSheet - MATH 352 FORMULA SHEET N P(exactly m of N...

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MATH 352 - FORMULA SHEET P (exactly m of N A i events occur) = N k = m ( 1) k m ( k m ) S k , P (at least m of N A i events occur) = N k = m ( 1) k m ( k 1 m 1 ) S k , where S k = 1 j 1 < ··· <j k N P ( A j 1 A j 2 · · · A j k ) DISCRETE DISTRIBUTIONS Name Probability Mass Function Mean Variance Bernoulli( p ) p x (1 p ) 1 - x , for x = 0 , 1 p p (1 p ) Binomial( n, p ) ( n x ) p x (1 p ) n - x , for x = 0 , 1 , . . . , n np np (1 p ) Geometric( p ) (1 p ) x - 1 p , for x = 1 , 2 , . . . 1 /p (1 p ) /p 2 Negative Binomial( r, p ) ( x - 1 r - 1 ) p r (1 p ) x - r , for x = r, r + 1 , . . . r/p r (1 p ) /p 2 Poisson( λ ) λ x x ! e - λ , for x = 0 , 1 , . . . λ λ Hypergeometric( n, K, N ) ( K x )(
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