Chapter%202%20-%20Extra%20Practice%20Problems

# Chapter%202%20-%20Extra%20Practice%20Problems - Econ 120B...

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Econ 120B Chapter 2 – Extra Practice Problems 1. Consider the following probability distribution: x p(x) 5 0.10 10 0.15 15 0.25 20 0.50 a. Calculate the expected value of the random variable. b. Let Y = X + 5. Calculate the expected value of the new random variable Y. c. Let Z = 5 X. Calculate the expected value of the new random variable Z. d. From your calculations in part a. and b., indicate the effect that adding a constant to a random variable has upon the expected value of the random variable. e. From your calculations in part a. and c., indicate the effect that multiplying a random variable by a constant has upon the expected value of the random variable. 2. Consider the following probability distribution: x p(x) 3 0.13 6 0.12 9 0.15 12 0.60 a. Calculate the variance and standard deviation of the random variable. b. Let Y = X + 7. Calculate the variance and standard deviation of the new random variable Y. c. Let Z = 7 X. Calculate the variance and standard deviation of the new random variable Z. d. From your calculations in part a. and b., indicate the effect that adding a constant to a random variable has upon its variance and standard deviation. e. From your calculations in part a. and c., indicate the effect that multiplying a random variable by a constant has upon the variance and the standard deviation of the random variable. 3. Consider the following probability distribution: x 5 10 15 20 25 30 35 40 45 50 p(x) 0.01 0.05 0.14 0.20 0.30 0.15 0.05 0.04 0.01 0.05 a. Calculate the expected value and the standard deviation for this random variable. b. Denote the expected value as μ and the standard deviation as σ . Calculate μ σ and μ + σ . c. Determine the proportion of the distribution that is contained within μ σ and μ + σ . d. Repeat part c. for (1) μ – 2 σ and μ + 2 σ , and (2) μ – 3 σ and μ + 3 σ .

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4. The US Census Bureau (2004 Annual Social and Economic Supplement) collects demographics concerning the number of people in families per household. Assume the distribution of the number of people per household is shown in the following table: x p(x) 2 0.27 3 0.25 4 0.28 5 0.13 6 0.04 7 0.03 a. Calculate the expected number of people in families per household in the United States. b. Compute the variance and the standard deviation of the number of people in families per household. 5. A retail store keeps four alarm clock radios in stock. At the end of a week, the store restocks the item if it has fewer than four clock radios available. The amount that is restocked each week is the number of clock radios necessary to bring the in-stock level up to four. If weekly demand is greater than four units in stock, the store loses the sale. The radio sells for \$25 and costs the store \$15. The store
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## This note was uploaded on 07/01/2008 for the course ECON 120B taught by Professor Jeon during the Spring '08 term at UCSD.

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Chapter%202%20-%20Extra%20Practice%20Problems - Econ 120B...

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