Formulas ST 200 I - E X ± E Y V ar X ± Y = V ar X V ar Y...

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Descriptive statistics and standardization Sample Mean: x = x n Sample Variance: s 2 = ( x - x ) 2 n - 1 Sample Standard Deviation: s = s 2 z-score: z = x - μ σ Linear regression Correlation Coefficient: r = ( x - x )( y - y ) ( n - 1) s x s y Slope: b 1 = r s y s x Intercept: b 0 = y - b 1 x Regression Line : ˆ y = b 0 + b 1 x Probability Complement: P ( A c ) = 1 - P ( A ) Addition Rule: P ( A or B ) = P ( A ) + P ( B ) - P ( A and B ) Disjoint Events: P ( A and B ) = 0 Independent Events: P ( A and B ) = P ( A ) P ( B ) Conditional Probability: P ( A | B ) = P ( A and B ) P ( B ) Multiplication Rule: P ( A and B ) = P ( B ) P ( A | B ) Bayes’ Theorem: P ( B | A ) = P ( B ) P ( A | B ) P ( A ) Random Variables Expected value (mean): E ( X ) = μ = X xP ( X = x ) Variance: V ar ( X ) = σ 2 = X ( x - μ ) 2 P ( X = x ) 1
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Properties: E ( X ± c ) = E ( X ) ± c V ar ( X ± c ) = V ar ( X ) E ( aX ) = aE ( X ) V ar ( aX ) = a 2 V ar ( X ) E ( X ± Y ) =
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Unformatted text preview: E ( X ) ± E ( Y ), V ar ( X ± Y ) = V ar ( X ) + V ar ( Y ) if independent Geometric Model Model for: X = number of trials until the first success Distribution: P ( X = x ) = q x-1 p , x = 1 , 2 ,... Mean: μ = 1 p Standard Deviation: σ = r q p 2 Binomial Model Model for: X = number of successes in n Bernoulli trials Distribution: P ( X = x ) = n C x p x q n-x , x = 0 , 1 ,...,n Mean: μ = np Standard Deviation: σ = √ npq 2...
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This note was uploaded on 07/25/2008 for the course STT 200 taught by Professor Dikong during the Summer '08 term at Michigan State University.

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Formulas ST 200 I - E X ± E Y V ar X ± Y = V ar X V ar Y...

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