Mid2_formulas

Mid2_formulas - Population mean and variance of discrete...

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Unformatted text preview: Population mean and variance of discrete random variable formulas : Dispersion of linear combinations of random variables: 2 2 σ a +bX = b 2σ X 2 µ X = ∑ xi p i σ X = ∑ ( x i − µ ) 2 p i 2 2 2 2 2 2 σ X +Y = σ X + σ Y + 2 ρσ X σ Y σ X −Y = σ X + σ Y − 2 ρσ X σ Y 2 22 22 For a “weighted average” where a+b = 1: σ aX +bY = a σ X + b σ Y + 2 ρaσ X bσ Y If X1 & X2 are uncorrelated (so ρ = 0), then variance of a portfolio of n investments denoted X1, X2, X3, …Xn; each with 2 2 2 2 σ (21 / n ) X1 + σ (21 / n ) X 2 + ... + σ (21 / n ) X n = (1 / n) 2 σ X1 + (1 / n) 2 σ X 2 + ... + (1 / n) 2 σ X n = 1 n σ X P ( A ∩ B ) P ( B | A) ⋅ P ( A) P ( B | A) ⋅ P ( A) = = Bayes’ rule: P ( A | B ) = P( B) P( B) P( B | A) ⋅ P ( A) + P ( B | AC ) ⋅ P( AC ) n k n −k For X with Binomial distribution: μ = np ; σ2 = np(1-p) and the probability that X=k is p (1 − p ) k a 1/n share, is: () margin of error: m = z* σ n z- calculated = z= X − µ0 σ n Critical Zs: z .025 * = 1.96; z.*005 = 2.576 ...
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