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Econ375StudyProblems - Econ 375 Study Problems Burhan Biner...

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Econ 375 Study Problems Burhan Biner January 25, 2010 You can have a cheat sheet for the midterm exam. Please write whatever you deem necessary on both sides of an A4 paper. I am going to list a few problems that might be helpful for the exam. Mind you, you are responsible for everything we have done in class and on the homework assignments. Every problem I solved in class and assigned for homework are good study problems. You should have a look at the end of chapter problems in the Statistics lecture notes I posted on the blackboard. Some of the problems I am listing here are for after the midterm, we won’t be able to get to them before the midterm. Exercise 1 Solve problems B1, B2, B3, B4, B5, B6, B7, B8, B11, B12, B13 in Appendix B. Exercise 2 Solve problems C1, C2, C3, C4, C5, C6, C8, C9 in Appendix C. Exercise 3 Solve problems 2.2, 2.5, 2.6, 2.7, 2.8 in Chapter 2. Exercise 4 Explain why the following variables can be thought of as random vari- able: the gender of the next person you meet, the number of times a computer crashes, the time it takes to commute to school, whether the computer you are assigned in the library is new or old, whether it is raining or not. Exercise 5 Suppose that the random variables X and Y are independent and you know their distributions. Explain why knowing the value of X tells you nothing about the value of Y . Exercise 6 An econometrics class has 80 students, and the mean weight is 145 lbs. A random sample of 4 students is selected from the class and their average weight is calculated. Will the average weight of the students in the sample equal 145 lbs. Why or why not? Use this example to explain why the sample average, ¯ Y , is a random variable. Exercise 7 Let Y denote the number of heads that when two coins are tossed. Derive the probability distribution of Y . Derive the cumulative probability distribution of Y . Derive the mean and variance of Y . 1
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Exercise 8 Suppose X is a Bernoulli random variable with P ( X = 1) = p . Show E ( X 3 ) = p . Show E ( X k ) = p for k > 0 . Suppose that p = 0 . 3 . Compute the mean, variance, skewness and kurtosis of X . Exercise 9 In September, Seattle’s daily high temperature has a mean of 70 F and standard deviation of 7 F . What is the mean, standard deviation and variance in C . Exercise 10 The following table gives the joint probability distribution between employment status and college graduation among those either employed or looking for work (unemployed) in the working age U.S. population, based on the 1990 U.S. Census. Joint Distribution of Employment Status and College Graduation in the U.S. Population Aged 25-64, 1990 Unemployed ( Y = 0) Employed ( Y = 1) Total Non-college grads ( X = 0 ) 0.045 0.709 0.754 College Grads ( X = 1) 0.005 0.241 0.246 Total 0.050 0.950 1.00 Compute E ( Y ) . The unemployment rate is the fraction of the labor force that is unemployed.
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