PS3 - Problem Set 3 Econometrics 120A Due Friday Nov 12 1...

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Problem Set 3 - Econometrics 120A Due Friday Nov 12 1. Suppose you have a sample of n observations { X i } n i =1 , and we are interested in learning about the population mean μ . (a) A researcher decides to estimate μ by looking at the sample average over the first half of the sample (Assume n is even). Denote this estimator by ˆ μ 1 = 1 n/ 2 n/ 2 i =1 X i . What is the expectation of ˆ μ 1 ? What is the variance of ˆ μ 1 ? (b) How does the estimator in (a) compare to the average over the whole sample? Which one would you use? 2. Computer Problem. We are going to do a Monte Carlo by generating random variables and examining sample means. There is a function in the Data Analysis Toolpak (look in the TOOLS menu for DATA ANALYSIS, if it is not there see the introduction in EXCEL hints) that computes draws from random variables for us. The experiment I want to do is to examine the distribution of the sample mean from Bernoulli random variables with π =0.5. We will generate 100 samples with n=20, so we can compute 100 sample means and draw a histogram of these. To do this, follow these steps:
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