11ProbHw5 - IEOR 3658 Probability Prof. Mariana...

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IEOR 3658 Assignment #5 Probability October 12, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #5 – due October 19th, 2010 1. (From text) A stock market trader buys 100 shares of stock A and 200 shares of stock B. Let X and Y be the price changes of A and B, respectively, over a certain time period, and assume that the joint PMF of X and Y is uniform over the set of integers x and y satisfying - 2 x 4 , - 1 y - x 1 . (a) Find the marginal PMFs and the means of X and Y . (b) Find the mean of the trader’s profit. 2. (From text) A class of n students takes a test consisting of m questions. Suppose that student i submitted answers to the first m i questions. (a) The grader randomly picks one answer, call it ( I,J ), where I is the student ID number (taking values 1 ,...,n ) and J is the question number (taking values 1 ,...,m ). Assume that all answers are equally likely to be picked. Calculate the joint and the marginal PMF of I and J . (b) Assume that an answer to question
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11ProbHw5 - IEOR 3658 Probability Prof. Mariana...

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