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Recitation_Problems 9.18.09

Recitation_Problems 9.18.09 - for x = 1 2 3 4 5 = 0...

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Recitation Problems for September 18, 2009 Instructor’s Problems 1) Consider the following probability mass function for the discrete random variable, X: p(x)= k (1 + x 2 ) for x = 1, 2, 3 p(x) = 0, otherwise. a) Find the value for k. b) Find the probability that X is less than or equal to 2. c) Find the mean and variance for X. 2) Consider the following probability density function for the continuous random variable, X: f ( x ) = 6x 5 for 0 < x < 1 f ( x ) = 0 otherwise. a) Find the probability that 0.5 < X < 1. b) Find the cumulative probability distribution function, F(x). c) Find the mean and standard deviation of X. Group Problems 1) For a particular illness the number of days of hospitalization, X, is a discrete random variable with probability mass function, P (X=x) = p(x) = (6-x)/15
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Unformatted text preview: for x = 1, 2, 3, 4, 5 = 0 otherwise a) Determine the mean and standard deviation for the days of hospitalization for this illness. b) Determine the value of the cumulative distribution function for X= 3 days. c) Find the expected value of Y = 2X 2 +3X -5 2) Let probability density function of X be given by, f (x) = cx(2-x) for 0 < x < 2, = 0 otherwise a) What is the value of c? b) Compute P(X < 1.5). 3) A box of widgets contains four good ones and one defective. To locate the defective widget, one widget at a time is drawn at random from the box (and not replaced) and then tested. Let X denote the number of tests required to locate the defective widget. a) Determine the probability mass function of X. b) Find the expected value for X....
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