FORMULAS on midterm 2(given)

FORMULAS on midterm 2(given) - The following formulas below...

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Unformatted text preview: The following formulas below may be of use. 2 2 σ a +bX = b 2σ X 2 2 2 σ X +Y = σ X + σ Y + 2 ρσ X σ Y 2 2 2 σ X −Y = σ X + σ Y − 2 ρσ X σ Y 2 22 22 For “weighted average” σ aX +bY = a σ X + b σ Y + 2 ρaσ X bσ Y where a+b = 1 If X1 & X2 are uncorrelated (so ρ = 0), then variance of a portfolio of n investments denoted X1, X2, X3, …Xn; each 2 2 2 with a 1/n share, is: 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 For X with binomial distribution: μ = np ; σ2 = np(1-p) and the probability that X=k is: P (X = k) = ⎜ ⎟ p k (1 − p ) n − k ⎜k ⎟ ⎛n⎞ ⎝⎠ ˆ For sample proportion, p-hat, p : μ = p and σ = p (1 − p ) n Bayes’ rule: P ( D | S ) = P( S | D) ⋅ P( D) P( S | D) ⋅ P( D) + P( S | D C ) ⋅ P( D C ) ...
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