Let Z1 and Z2 be independent standard normal N(0, 1) random variables. Let X = Z1 + 2Z2, and let Y = 2Z1 + Z2. a. Find rho( X, Y ) = correlation of X and Y. b. Find the numerical value of P{ X > 0 and Y > 0 }.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Let Z1 and Z2 be independent standard normal N(0, 1) random variables. Let X = Z1 + 2Z2, and let Y = 2Z1 + Z2. a. Find rho( X, Y ) = correlation of X and Y. b. Find the numerical value of P{ X > 0 and Y > 0 }. HINT: Use trigonometry.
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