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formulaMT1 (6)

formulaMT1 (6) - μ x = ∑ i x i f x i • Standard...

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Kata Bognar [email protected] Economics 41 Statistics for Economists UCLA Fall 2010 Formula Sheet Descriptive measures Mean: μ = i x i n Standard deviation: σ = q i ( x i - μ ) 2 N z-Score: z i = x i - μ σ Probability Probability for equally likely outcomes: P ( A ) = N ( A ) N Complementation rule: P ( A 0 ) = 1 - P ( A ) Addition rule: P ( A B ) = P ( A ) + P ( B ) - P ( A B ) Conditional probability rule: P ( B | A ) = P ( B A ) P ( A ) Multiplication rule: P ( A B ) = P ( B ) × P ( A | B ) Rule of total probability: P ( A ) = i P ( A | B i ) P ( B i ) Bayes’s Theorem: P ( B k | A ) = P ( A | B k ) P ( B k ) i P ( A | B i ) P ( B i ) Factorial: k ! = k × ( k - 1) × · · · × 2 × 1 Permutation rule: n P r = n ! ( n - r )! Combination rule: n C r = n ! ( n - r )! r ! Binomial coefficient: ( n x ) = n ! ( n - x )! x ! Random variables Mean of a discrete random variable:
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Unformatted text preview: μ x = ∑ i x i f ( x i ) • Standard deviation of a discrete random variable: σ x = p ∑ i ( x i-μ ) 2 f ( x i ) • Mean of an empirical distribution: ¯ x = ∑ i x i h ( x i ) • Standard deviation of an empirical distribution: s = q n n-1 ( ∑ i ( x i-¯ x ) 2 h ( x i )) • Binomial probability formula: f ( x ) = ( n x ) p x (1-p ) n-x • Mean of a binomial random variable: μ = np • Standard deviation of a binomial random variable: σ = p np (1-p ) 1...
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