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270 formulas - Binomial N trials S or F Independent Same...

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Binomial N trials;S or F ; Independent; Same Probability pmf :b x ;n , p , = n x p x ⋅ 1 p n x cdf : p X x = B x ;n , p = y = 0 x b y ;n, p, V x = n p ⋅ 1 p E x = np p = x n isan unbiasedestimator Hypergeometric N in pop ,n in sample;S or F , M S' s ;no replacement P X = x = h x ;n, M , N = M x ⋅ N M n x N n E x = n ⋅ M N V x = N n N 1 n ⋅ M N ⋅ 1 M N Negative Binomial independent trials; S or F; Prob of S const Exp continues until r S's pmf :nb x ;r , p = x r 1 r 1 p r ⋅ 1 p x E x = r ⋅ 1 p p V x = r ⋅ 1 p p 2 Poisson Dist P X ;  = e − ⋅ x x! E x = V x = P k t = e −⋅ t ⋅⋅ t k k ! =⋅ t ;t = time = expected amount time t GammaDist = 0 x  − 1 e x dx f x ; , = 1 ⋅ x − 1 e x x 0 ;  0 ;  0 Standard : = 1 E x =⋅ V x =⋅ 2 P X x = F x ; , = F x ,  F x ; = 0 x y − 1 e y   dy Exp Dist f x ; =⋅ e −⋅ x x 0 E x = 0 x ⋅⋅ e −⋅ x dx = 1 2 = 1 2 F x ;  = { 0 x 0 1 e −⋅ x x 0 } Weibull f x ; , = x − 1 e − x x 0 =⋅ 1 1 2 = 2 ⋅[  1 2 − 1 1  2 ] F x ; , = 1 e − x x 0 Lognormal f x ; , = 1 2 ⋅⋅ x e [ − ln x − ] 2 2 2 ∧ for ln x E x = e  2 2 V x = e 2   2 ⋅ e 2 1 F x , , = ln x − x 0 ChiSquared = 2 = 2 = degrees of freedom f x ; = 1 2 2 ⋅ 2 x 2 − 1 e x 2 x 0 Beta Dist f x ; , , A, B = 1 B A  ⋅ ⋅ x A B A − 1 ⋅ B x B A − 1 Standard: A = 0, B = 1 = A  B A ⋅  2 = B A 2 ⋅⋅   2   1 Normal Dist f x ; , = 1 2 ⋅ e − x − 2 2 2 z = x − 1 SD = 68%, 2 SD = 95%, 3 SD = 99.7% f z ; 0,1 = 1 2 e z 2 2 Std Normal cdf of z is P Z z = − ∞ z f y , 0, 1 dy = z P a x b =[ a − ≤ z ≤ b − ]= b − −  a − =  X is MVUE for ContinuousVariables pmf : f x P A x B = A B f x dx cdf :F x − −∞
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