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ISyE 6644 — Summer 2020 — Test #2 Solutions (revised 6/29/20)

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Crop Protection

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Chemistry

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Questions and Answers

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14

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ATIPROS

This test is 120 minutes. All questions are each worth 3 points. Let’s get some lawyer stuff out of the way. . . You’re allowed the following items: • Pencil / pen and scratch paper. • A reasonable calculator. • Two cheat sheets (4 sides total). • Normal, t, and χ2 tables. (I will supply these.) Good luck! I want you to make this test sorry that it ever tried to mess around with you!!! 1. Suppose X and Y are discrete random variables with the following joint p.m.f. f (x, y) X = 2 X = 3 Pr(Y = y) Y =0 0.2 0.5 0.7 Y =1 0.0 0.3 0.3 Pr(X = x) 0.2 0.8 1.0 Find Var(X − Y ). (a) 0.06 (b) 0.16 (c) 0.21 (d) 0.25 (e) 0.49