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Unformatted text preview: 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 | ≥ kσ ) ≤ 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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This note was uploaded on 04/23/2011 for the course STAT 416 taught by Professor Staff during the Spring '08 term at Purdue University.
- Spring '08