ISyE 6644 Fall 2020 Test #2b Solutions Midterm II Solutions

(Revised 11/6/20) This test is 120 minutes. There are 38 questions, each worth 2.5 points, and a “free” 39th question, worth 5 points (total = 100). In additon, later on, we will add 4 points to everyone’s score (up to a max of 100). But in exchange, you will not be allowed to whine about (and we will not consider) any grade scoring issues unless they involve more than 4 points. Let’s get some additional awyer 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.) But note that • You are not allowed to use Arena, even though I’m asking questions about it. • This test requires some sort of proctor. • If you encounter a ProctorTrack issue, contact us immediately (but don’t get an ulcer over it). 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 continuous random variables with joint p.d.f. f (x, y) = cxy 2 , 0 ≤ x ≤ 2, 0 ≤ y ≤ 1, for some appropriate constant c. Find E[2X − 1]. (a) 1/6 (b) 5/3 (c) 5/2 (d) 11/3