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Unformatted text preview: ISyE 2027 Probability with Applications Polly B. He Fall10, Week 14 Reading: Section 11.1-11.2 (expect the subsection on “single-server queue revisited”) Sums of Discrete Random Variables Motivating Example 1: Suppose you are on a cross-country road trip and you have one GPS device installed on your car and another GPS you carry for backup. Each day the GPS installed on the car may fail with probability p . Once it fails, you switch to the backup unit. How certain are you that the two GPS devices won’t fail before the end of the trip? Rule for adding two independent discrete R.V.’s: Let X and Y be two independent random variables, with probability mass functions p X and p Y . Then the probability mass function p Z of Z = X + Y satisfies p Z ( c ) = ∑ j p X ( c- b j ) p Y ( b j ) where the sum runs over all possible values b j of Y . Example 11.1.1 Suppose we roll a dice twice and let the sum of the two outcomes be S = X + Y , where X and Y are the outcomes of the first and second rolls, respectively.are the outcomes of the first and second rolls, respectively....
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- Fall '08
- Normal Distribution, Probability theory, probability density function