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Lecture8_print

# Lecture8_print - MA/STAT416 Probability Lecture Notes...

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MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 4: Discrete Random Variables and Mass Functions March 7, 2011 4.5 Uses of μ and σ as Summaries; Markov and Chebyshev’s Inequality Theorem 1 (Chebyshev’s Inequality) . Suppose E ( X ) = μ and V ar ( X ) = σ 2 are as- sumed to be finite. Let k be any positive number. Then, P ( | X - μ | ≥ ) 1 k 2 . Example 2 . Find the variance and standard deviation of the sum of the scores in rolling a fair die twice. How much of the probability distribution falls within two sigma from the mean? Three sigma from the mean? Compute the Chebyshev bound for the two sigma and the three sigma interval around the mean. Compare the bound with the exact value of those probabilities. Example 3 . Find the variance and standard deviation of the number of aces in a hand of 4 cards drawn randomly from a deck of 52 cards. How much of the probability distribution falls within two sigma from the mean?
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