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Section4 - Statistics 104 Spring 2011 Section#4 Topics for...

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Statistics 104 – Spring 2011 Section #4 Topics for Section Random Variables Discrete vs. Continuous Expectations Means, Variances, Linear Combinations of Independent RV's Covariance, Correlation Joint and Conditional Probability Distributions Binomial, Poisson Random Variables Practice Problems 1. Let X denote the number of touchdowns the Patriots will score in any given quarter, and Y the number of touchdowns their opponent scores in any given quarter. Below is the table of joint probabilities for these two random variables, touchdowns by quarter. Patriots Opponent 0 1 2 0 0.2 0.19 0.06 1 0.22 0.09 0.09 2 0.03 0.12 0.00 a. How would you confirm that this is a valid probability distribution? b. Find the marginal distribution of X. What are the mean and standard deviation of X? c. Find the marginal distribution of Y. What are the mean and standard deviation of Y? d. How would you show if X and Y independent? Are they independent? (Baxter's Metatheorem!)
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e. What is the covariance between X and Y? What is the correlation between the number of touchdowns the Patriots and their opponents score?
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