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Econ 210 Spring 2009 Problem Set 4

Econ 210 Spring 2009 Problem Set 4 - score can the firm...

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Econ 210 Spring Quarter 2009 Problem Set 4 - Due Date: 5/6/2009 1. TRUE/FALSE a. The sample mean is a random variable b. One drawback of the sample median is that it is very sensible to the inclusion of outliers in the sample. c. Consider X~N(5,100). The interquartile range is equal to 1.35 d. Let X follow a Chi-squared distribution with 5 degrees of freedom. Then P(X<11)=0.99 2. Calculate the following Probabilities a. If Y~N(2,4) calculate Pr(Y<3) b. If Y~N(4,9) calculate Pr(Y>0) c. If Y~N(8,2) calculate Pr(6<Y<8) d. If Y~N(8,2) calculate Pr(8>Y>6) 3. What does i.i.d mean? Explain using an example. 4. What are the 3%, 15%, 20% one- and two-sided critical values of the standard normal distribution. 5. There are 5000 people in the population and their IQ test scores are normally distributed with mean 100 and standard deviation 20. If a firm wants to hire 500 people how high of a test
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Unformatted text preview: score can the firm require from their applicants? 6. Consider a portfolio consisting of two assets X and Y. Asset X has a mean return of 4% and a standard deviation of 10. Asset Y has a mean return of 12% and a standard deviation of 15. You have invested 70% of your money in asset X and 30% in asset Y. Assume that Cov(X,Y)=75. Assume both X and Y are normally distributed. a. What is the probability that the portfolio’s return is positive? b. What is the probability that the portfolio loses at most 5%? c. What is the probability that the portfolio’s return is between 10% and 20% 7. Assume you have taken a sample of size N=30 with 195 , 30 = ∑ and 825 = i 1 2 = N i i X 1 ∑ = N i X a. Find the sample mean b. Find the sample variance (hint: expand the formula we know)...
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