fnlsolns

fnlsolns - University of Illinois at Chicago School of...

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University of Illinois at Chicago School of Public Health Division of Epidemiology & Biostatistics BSTT 580 Applied Multivariate Statistical Analysis Instructor Stan Sclove Textbook Johnson & Wichern, 4th ed. (JW) SOLU TIONS TO FINAL EXAM / 10:00 - 11:45, Wed., 6-Dec-2000 "Open book": Use of books and notes is permitted. One hour, forty-five minutes. Four parts, 25 points each, 100 points total. Any undefined notation is that of JW . Part 1. Covariance 1.1. [4 pts.] Var(X+Y) = Var(X) + Var(Y) + c Cov(X,Y). c = ? ___2____ 1.2. [4 pts.] Var(X-Y) = Var(X) + Var(Y) + c Cov(X,Y). c = ? __ -2_____ 1.3. [4 pts.] Cov(X+Y,X-Y) = Var(X) + cVar(Y). c = ? ___-1____ 1.4. [4 pts.] Cov(X,Y) = c [Var(X+Y) - Var(X-Y)] . c = ? __1/4_______ 1.5. [4 pts.] Var(2X+3Y) = aVar(X) + bVar(Y) + cCov(X,Y). a = ? _4__ b = ? _9 __ c = ? _12___ 1.6. [5 pts.] Let β = Cov(X,Y)/Var(X). Cov(X, Y - β X) = ? ___ zero _______________ Comment. The residual variable is uncorrelated with the response variable.
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BSTT 580 / FALL, 2000 / SCLOVE / SOLUTIONS TO FINAL EXAM p. 2 Part 2. Conditional Distribution in a Bivariate Normal Distribution Suppose H and W are jointly normally distributed, with parameters μ H = 68", σ H = 3.0", μ W = 165 lbs., σ W = 20 lbs. , ρ HW = +.6. 2.1.
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fnlsolns - University of Illinois at Chicago School of...

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