t2s07_retake[1]

# t2s07_retake[1] - 1 NAME ISyE 3770 Retake of Test 2 Spring...

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1 NAME ISyE 3770 — Retake of Test 2 Spring 2007 This is a take-home test and should not take more than a couple of hours. Show all work, write incredibly neatly, and clearly indicate your answers. Turn the test in at the beginning of class on Tuesday April 24. 1. If X is a random variable with c.d.f. F ( x ) = 1 - e - λx , x 0, ﬁnd E [ x 3 ]. (This may take a little calculus.) 2. If X is a random variable with m.g.f. 0 . 7 e t + 0 . 3, ﬁnd E [ X 2 ]. 3. If X is a random variable with m.g.f. 0 . 7 e t + 0 . 3 and Y = 2 X + 1, ﬁnd the m.g.f. of Y . 4. If X , Y , and Z are i.i.d. with m.g.f. 3 / (3 - t ), what’s the m.g.f. of X + Y + Z ? 5. True or False? Suppose that X and Y have joint p.d.f. f ( x,y ) = cx 2 / (1 + x + y ), 1 x 2, 1 y 3, where c is the appropriate constant. Then X and Y are independent. 6. True or False? Suppose that X and Y have joint p.d.f. f ( x,y ) = cx 2 / (1+ x + y ), 1 x y 2, where c is the appropriate constant. Then X and

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t2s07_retake[1] - 1 NAME ISyE 3770 Retake of Test 2 Spring...

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