STSCI 4740

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STSCI 4740 Machine Learning and Data Mining_HW1_solutions Cornell University STSCI 4740

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STSCI 4740 Machine Learning and Data Mining Fall Dr. Yang Ning Homework 1 Problem 1 (6 points) 1. Express Var(X1 X2) through the variances and covariances of X1, X2 (assuming all variances exist). Answer: Var(X1 X2) = E((X1 X2) 2) (E(X1 X2))2 = E(X2 1 ) 2E(X1X2) + E(X2 2 ) E(X1) 2 + 2E(X1)E(X2) E(X2) 2 = Var(X1) + Var(X2) 2Cov(X1, X2) 2. Assume that X1, ..., Xn are i.i.d. real-valued random variables with finite variances. Show that Var⇣ 1 n Xn i=1 Xi ⌘ = ...

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