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crib_sheet1 - Crib Sheet for Exam #1 Statistics 211 1...

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Unformatted text preview: Crib Sheet for Exam #1 Statistics 211 1 Chapter 1: Descriptive Statistics Sample Average Population Average ¯ x = 1 n ∑ n i =1 x i μ = 1 N ∑ N i =1 x i To caluclate the p ’th percentile x [ p ] : 1. Let x ( i ) refer to our data set in ascending order. 2. Let i p = np/ 100. 3. Find the first index i such that i > i p . 4. The p ’th percentile is then: x [ p ] = x ( i- 1) + x ( i ) 2 if i- 1 = i p x ( i ) otherwise s 2 = 1 n- 1 X ( x i- ¯ x ) 2 = 1 n- 1 X x 2 i- (∑ x i ) 2 n Chebychev’s Rule: The proportion of observations that are within k standard deviations ( p k ) of the mean is at least: p k = 1- 1 k 2 2 Chapter 2: Probability Multiplication rule Permutation Combination n 1 × n 2 × n 2 ... × n k P k,n = n ! ( n- k )! ( n k ) = P k,n k ! = n ! k !( n- k )! For any two events A and B : P ( A ∪ B ) = P ( A ) + P ( B )- P ( A ∩ B ) The conditional probability of A given that B occurred ( P ( B ) > 0): P ( A | B ) = P ( A ∩ B ) P ( B ) Two events A and B are independent if P ( A | B ) = P ( A ) If A and B are independent then P ( A ∩ B ) = P ( A ) P ( B ) If A,B,C,D,... are mutually independent then P ( A ∩ B ∩ C ∩ D ... ) = P ( A ) P ( B ) P ( C ) P ( D ) ... 1 3 Chapter 3: Discrete PDF’s E [ X ] = μ = X X ∈ S x · p ( x ) E [ h ( X )] = μ h ( x ) = X X ∈ S h ( X ) · p ( x ) E ( aX + b ) = aE ( X ) + b V ( X ) = σ 2 = E [( x- u ) 2 ] = ∑ X ∈ S ( x- μ ) 2 · p ( x ) = E [ X 2 ]- E [ X ] 2 V ( aX + b ) = a 2 V ( X ) = a 2 σ 2 3.1 Binomial Distribution For X ∼ binomial( n,p ) n = fixed number of trials p = probability of succes ( S ) x = number of successes ( S ) P ( X = x ) = n x p x (1- p ) n- x x = 0 , 1 , 2 ,...,n μ = E [ X ] = np σ 2 = V [ X ] = E [( x- μ ) 2 ] = np (1- p ) 3.2 Multinomial Distribution For X ∼ multinomial(...
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This note was uploaded on 03/29/2008 for the course STAT 211 taught by Professor Parzen during the Spring '07 term at Texas A&M.

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crib_sheet1 - Crib Sheet for Exam #1 Statistics 211 1...

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