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# hw2 - (b If selected ball is blue ﬁnd the probability...

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IE 336 Handout #3 Sep. 12, 2008 Due Sep. 19, 2008 Homework Set #2 1. Consider a group of n chips. A chip can be either good or bad. Assume that a chip is good with probability 3 4 . (a) Find the probability that a randomly selected chip is bad. (b) Find the probability that the number of bad chips is less than 4. (c) Find the expected value of the number of bad chips. 2. Let X be uniform random variable. Also, let E ( X ) = 2 , Var( X ) = 1 3 . Determine n such that E ( X n ) = 10. 3. There are two boxes with balls. One of the boxes is yellow the other one is green. There are 10 red and 20 blue balls in the yellow box and 15 red and 5 blue balls in the green box. First a box is selected at random and from the selected box a ball is selected at random.
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Unformatted text preview: (b) If selected ball is blue 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 green box. 4. Let X be binomial random variable with parameters n = 5 and p = 0 . 2. Compute E ((3 X + 1) 2 ). 5. Let X be normally distributed random variable with parameters μ and σ 2 , i.e. E ( X ) = μ, Var( X ) = σ 2 . Further, let Y be uniform random variable deﬁned on the interval [ a,b ], i.e., p ( y ) = ( 1 b-a a ≤ y ≤ b otherwise . Assuming that X and Y are independent ﬁnd E ((7 X-2 Y-1 ) 2 ). 1...
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