# Hw2 - (b If selected ball is red ﬁnd the probability that it was selected from the yellow box(c If selected ball is blue ﬁnd the probability

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IE 336 Handout #3 Jan. 28, 2011 Due Feb. 4, 2011 Homework Set #2 1. Consider a group of n (say n > 1000) chips. Each chip in the group can be either good or bad. Assume that each of the chips is good with probability 2 5 . (a) Find the probability that the number of good chips is greater than 4 and less than 8. (b) Find the expected value of the number of good chips. (c) Four chips are selected at random. Compute the probability that exactly three of the selected chips are bad. 2. Let X be a continuous uniform random variable. Also, let E ( X ) = 2 , Var( X ) = 1 3 . Determine n such that E ( X n ) = 10. 3. There are three boxes with balls. The ﬁrst box is yellow, the second box is green, and the third box is white. There are 7 red and 15 blue balls in the yellow box, 5 red and 3 blue balls in the green box, and 11 red and 6 blue balls in the white box. First a box is selected at random and then from the selected box a ball is selected at random. (a) If selected box is green ﬁnd the probability that the selected ball is blue.
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Unformatted text preview: (b) If selected ball is red ﬁnd the probability that it was selected from the yellow box. (c) If selected ball is blue ﬁnd the probability that it was selected from the white box. 4. Let f ( x,y ) = ce-x 2 + y 2-2 x-7 y 2 ,-∞ ≤ x,y ≤ ∞ , be the joint pdf of random variables X and Y . (a) Determine the value of the constant c . (b) Are X and Y independent random variables? Explain. (c) Compute E ( Y 2 + X 2 Y ). 5. Let X be exponentially distributed random variable with parameter λ . Clearly, f ( x ) = λe-λx ,x ≥ 0. Further, let Y be uniform random variable deﬁned on the interval [ a,b ], i.e., p ( y ) = ( 1 b-a a ≤ y ≤ b otherwise . Let Z be the standard normal random variable with pdf f ( z ) = 1 √ 2 π e-z 2 2 ,-∞ ≤ z ≤ ∞ . Assuming that X , Y , and Z are independent ﬁnd E ((2 XZ-4 Y-1 ) 2 + XY + Z 2 √ Y ). 1...
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## This note was uploaded on 05/06/2011 for the course IE 336 taught by Professor Bruce,s during the Spring '08 term at Purdue University-West Lafayette.

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