ARE106SU09HW1

ARE106SU09HW1 - 1 University of California, Davis...

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1 University of California, Davis Managerial Economic(ARE) 106, Summer 2009 Instructor: John H. Constantine Problem Set #1: Due Thursday, August 6, 2009 Problem 1 : The probability density function (pdf) for the monthly sales of luxury cars ( X ) at a particular dealership is: x 0 1 2 3 4 f(x) 0.10 0.30 0.25 0.20 0.15 (a) What is the probability of selling at least two cars in the next month? (b) Find the mean monthly sales. (c) Find the variance and standard deviation of sales. (d) Suppose that the monthly profit (in thousands of dollars) is given by: Profit = -5 + 8 x . Find the mean and standard deviation of monthly profit. Problem 2 : Based on long years of experience, an instructor at a local college has determined that in her class the probability distribution of X, the number of students absent on Mondays, is as follows: x 0 1 2 3 4 5 6 7 f(x) 0.005 0.025 0.310 0.340 0.220 0.080 0.019 0.001 (a) Sketch the probability distribution for X. (b) Find the probability that on a given Monday either 2, or 3, or 4 students will be absent. (c) Find the probability that on a given Monday more than three students will be absent. (d) Compute the expected value of random variable X. Interpret this result. (e) Compute the (i) variance and (ii) standard deviation of random variable X. (f) Compute the expected value and variance of Y = 7X + 3.
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This note was uploaded on 11/19/2009 for the course ARE ARE106 taught by Professor Constantine during the Spring '09 term at UC Davis.

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ARE106SU09HW1 - 1 University of California, Davis...

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