# Mterm2p_09 - Practice Midterm Exam Questions Second Midterm...

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Practice Midterm Exam Questions - Second Midterm Two Random Variable Questions. 1. Using the distribution in Question 5-12, part c) (p168) a) Work out the mean and variance of (X+Y). b) Work out the mean and variance of X, then the variance of Y. c) What is the relationship between the answers in a) and b)? (Note: This is simply done using the spreadsheet, where you can set up tables for each distribution and use the copy command and the fill down command to quickly replicate similar instructions. I will make such questions simple to calculate on an exam). 2. Suppose that the random variable X measures number of hamburgers purchased in a restaurant in an hour and Y measures the number of packages of antacid purchased in the convenience market next door in the same hour. The correlation between the two variables is 0.75. (a) Interpret what this correlation tells us about the relationship between the number of hamburgers purchased and the number of antacids purchased (be thorough in your answer). (b) Suppose the variance of X and the variance of Y are both equal to 16. What is the covariance between X and Y. (c) What is the variance of (X + Y)? 3. The joint distribution of two random variables X and Y is given by Y X 1 2 1 0.05 0.05 2 0.5 0.3 3 0.05 0.05 (a) What is the marginal distribution of X? (b) What is the mean of X?

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Mterm2p_09 - Practice Midterm Exam Questions Second Midterm...

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