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Unformatted text preview: IE 111 NAME ____Solutions_____________ 10:00 Section Exam 2 Fall 2007 Average = 77.8 SD = 18.2 Median = 88 N = 32 30's 44 40's 18 50's 69 60's 7 70's 1669 80's 245688999 90's 11224469 Question 1. A die has 4 sides (not 6 like a regular die). The four sides are labeled 1, 3, 5, and 10 respectively. It is equally likely that you will get a 1 or a 3. It is equally likely that you will get a 5 or a 10. It is twice as likely that you will get a 5 or10 than a 1 or 3. a) Let X = the outcome of a roll of the die. Find the probability mass function of X. x 1 3 5 10 f X (x) p p 2p 2p 6p=1 thus p=1/6 b) Find E(X) E(X) = (1/6)[ (1)(1) + (3)(1) + (5)(2) + (10)(2) ] = (1/6)(34) = 5.6667 c) If Y=2X 2 +1, find E(Y) E(X) = (1/6)[ (3)(1) + (19)(1) + (51)(2) + (201)(2) ] = (1/6)(526) = 87.6667 d) If I roll the die 10 times, what is the probability I get exactly 3 tens? 10 C 3 (1/3) 3 (2/3) 7 = 0.260123 Question 2 ....
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 Spring '07
 Storer

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