PS1_ans - Department of Economics University of California...

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Department of Economics Fall 2007 University of California Prof. Woroch Economics 140: Problem Set 1 Answer Sheet Instructions: Include names and SIDs of the members of your study group and the name of the single GSI for all of you. When asked to solve a question using Excel, write the final answer on your answer sheet and also attach a printout of the relevant portion of the Excel file. Include all intermediate steps and indicate clearly the final solution ( i.e. different color, box, etc.). Staple your answer sheets—otherwise it will not be accepted. 1. A damaged coin comes up “heads” with probability p = 3/5 and “tails” with probability 1 – p = 2/5. Suppose this coin is tossed twice. Let M denote the number of heads realized by the two flips. a) List all possible outcomes for M and the associated probability of each one. b) Using Excel, generate 50 trials of this simple experiment (i.e., two flips of the damaged coin). [Hint: used the =RAND() function in Excel.] c) Using the data you generated, use Excel to graph the “probability density function” (p.d.f.) for this experiment and the corresponding “cumulative distribution function” (c.d.f.), placing the values of M on the x-axis and probability values on the y-axis. d) Compute the sample mean and sample standard deviation of your synthesized data, and compare to the population mean and standard deviation of the random variable M. e) Given your synthesized data, what are the population and sample values for the probabilities of the following outcomes? i) Pr( M = 0) ii) Pr( M = 0 or M = 1) iii) Pr( M = 1 or M 2) ANSWER: a) M 0 1 2 Pr(M) 4/25 12/25 9/25 b) See Excel answer sheet. c) See Excel answer sheet d) The value in sample changes depending on the random number. See excel answer sheet. Population Sample E(M) 1.2 1.26 Std Dev(M) 0.48 0.69 e) Population Sample Pr(M = 0) 4/25 = 0.16 0.22 Pr(M = 0 or M = 1) 16/25 = 0.64 0.6 Pr(M = 1 or M 2) 16/25 0.6
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2 2. Download the Excel spreadsheet file called PS1data.xls from the Resources section of bSpace. It contains a dataset with 261 observations. The variables are defined as: FEMALE: 1 if the individual is female and 0 if the individual is male. AGE: Age of the individual. COLLEGE: 1 if the individual has a college degree, 0 otherwise. YEAR: two years, 1992 and 1998. a) Use Excel to complete the following table: 1992 1998 Total Males Females Total Observations Average Age Median Age Std Dev of Age % College % College & Age>30 b) Use Excel to compute the sample covariance and sample correlation between FEMALE and COLLEGE for each of the two years. ANSWER: The values for the missing statistics are computed in the PS1 Excel answer sheet and reported below. Look at the cell contents to see the formula. a) b) Year 1992: Corr(Female,College) = 0.084 Cov(Female,College) = 0.0209 Year 1998: Corr(Female, College) = - 0.04 Cov(Female,College) = - 0.009 3. In 1998, the campus placement office of a large, public university conducted a survey of starting salaries of graduating economics majors. With the help of the registrar, they were able to anonymously match the reported salaries of 108 graduates with their cumulative GPA during their undergrad career.
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PS1_ans - Department of Economics University of California...

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