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Unformatted text preview: DEPARTMENT OF ECONOMICS ECON 131A YALE UNIVERSITY ECONOMETRICS & DATA ANALYSIS I FALL 2010 Assignment #2 Due Tuesday September 21 In Class The same rules apply as on the first assignment. You may work with a study group of your choice on this assignment. However, even if you work with others you must write up and submit your own assignment. You may do your work by hand or in Excel, and you may hand in either handwritten answers or typed answers. Your grade depends on (1) getting the answer right, and (2) showing how you arrived at a correct answer. Late assignments will not be accepted. 1. A broker receives orders from two clients to buy shares of Microsoft. The first client orders 0, 50, 200 or 300 shares with probabilities 0.1, 0.2, 0.3, and 0.4, respectively. The second client orders 0, 100, or 150 units with probabilities 0.2, 0.2 and 0.6, respectively. (a) The broker is interested in the expected value and the standard devia- tion of the total number of shares ordered together by the two clients. Which one (if any) can you compute from the data above? Carry out the calculations. (b) Suppose that orders from the two clients are independent. Can you now compute the expected value and the standard deviation of total orders? If so, what is the probability that total orders will be less than or equal to 100 shares? (c) Suppose that, in fact, the joint distribution of orders from the two clients is given by the following probability table: Client 2 100 150 0.05 0.04 0.01 0.10 Client 1 50 0.06 0.06 0.08 0.20 200 0.06 0.09 0.15 0.30 300 0.03 0.01 0.36 0.40 0.2 0.2 0.6 1 What is the covariance between the orders? What is the expected value and the standard deviation of total orders? What is the probability thatand the standard deviation of total orders?...
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- Variance, Probability theory