Stats Formula

# Stats Formula - Box plot : x i min | lower 4 th | median |...

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Unformatted text preview: Box plot : x i min | lower 4 th | median | upper 4 th | x i max ; outlier >1.5fs, extreme >3fs P&C : P k,n = n ! ( n " k )! C k,n = n ! ( n " k )! Independence : P(A|B) = P(A), P(A ∩ B) = P(A).P(B), for J-pdf: f(x,y)=f X (x).f Y (y) E(X) = x . p ( x ) " E[h(X)] = h ( x ). p ( x ) " E(aX+b) = a.E(X) + b V(X) = E(X- µ ) 2 = E(X 2 ) – [E(X)] 2 V(aX+b) = a 2 .V(X) Binomial Distribution , approximately N(np, √ npq) when np ≥ 10, nq ≥ 10 X~Bin(n,p) = n x " # \$ % & ’ p x (1 ( p ) n ( x , E(X) = np, V(X) = npq, P(X ≤ x) = B(X; n, p) on Table Hypergeometric Distribution (For S/F without replacement, when n/N > 0.05): X~h(x; n, M, N) = M x " # \$ % & ’ N ( M n ( x " # \$ % & ’ N n " # \$ % & ’ , E(X) = np, V(X) = N " n N " 1 # \$ % & ’ ( ) npq Negative Binomial Distribution (For fixed S (r=num of S), variable number of trials (x=num of trials)): X~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 Distribution : X~p(x;...
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## This note was uploaded on 04/30/2008 for the course STAT 412 taught by Professor Shun during the Fall '06 term at University of Michigan.

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