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Unformatted text preview: ORIE 361 – Homework 1 (Introduction to Probability Theory) Instructor: Mark E. Lewis due January 30, 2008 (drop box) This homework assignment is designed to give you some practice in probability. Some of the concepts should be review, others are leading you to what we will cover in class. Some problems may appear as examples in your text...you still need to do them. Answers. 1. Notice that the marbles are being drawn from the box with replacement. (a) Ω = { ( R,R ) , ( R,G ) , ( R,B ) , ( G,R ) , ( G,G ) , ( G,B ) , ( B,R ) , ( B,G ) , ( B,B ) } (b) Because each marble in the box is equally likely to be selected the probability of each point in Ω is 1 9 2. In order to make this a legitimate density, it must integrate to 1. (a) Integrating from 0 to 2 yields Z 2 f ( x ) dx = c [ x 2 x 3 3 ]  2 = c [4 8 3 ] = c [ 4 3 ] = 1 . Thus, c = 3 4 . (b) To compute the mean, we compute E X = Z 2 xf ( x ) dx = Z 2 3 4 x 2 (2 x ) dx = 3 4 [2 x 3 / 3 x 4 / 4]  2 = 3 4 [16 / 3 4] = 1 ....
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 Spring '07
 LEWIS,M.
 Conditional Probability, Probability, Probability theory, dx, moment generating function, Mark E. Lewis

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