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HW sol - CDF Mean and Variance of Discrete Random Variables...

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Unformatted text preview: CDF, Mean, and Variance of Discrete Random Variables Andrew Liu September 14, 2011 Andrew Liu CDF, Mean, and Variance of Discrete Random Variables Review of Probability Mass and Cumulative Distribution Functions Andrew Liu CDF, Mean, and Variance of Discrete Random Variables Cumulative Distribution Function – Examples E.g. 1. (Textbook Example 3-7) Determine the probability mass function of X from the following cumulative distribution function. F ( x ) = x <- 2 . 2- 2 ≤ x < . 7 0 ≤ x < 2 1 2 ≤ x Andrew Liu CDF, Mean, and Variance of Discrete Random Variables Cumulative Distribution Function – Examples E.g. 1. (Textbook Example 3-7) Determine the probability mass function of X from the following cumulative distribution function. F ( x ) = x <- 2 . 2- 2 ≤ x < . 7 0 ≤ x < 2 1 2 ≤ x It doesn’t provide explicitly the range of X . Andrew Liu CDF, Mean, and Variance of Discrete Random Variables Cumulative Distribution Function – Examples E.g. 1. (Textbook Example 3-7) Determine the probability mass function of X from the following cumulative distribution function. F ( x ) = x <- 2 . 2- 2 ≤ x < . 7 0 ≤ x < 2 1 2 ≤ x It doesn’t provide explicitly the range of X . It doesn’t matter here! Probability mass function at each point = change of cumulative distribution function. Andrew Liu CDF, Mean, and Variance of Discrete Random Variables Cumulative Distribution Function – Examples E.g. 1. (Textbook Example 3-7) Determine the probability mass function of X from the following cumulative distribution function. F ( x ) = x <- 2 . 2- 2 ≤ x < . 7 0 ≤ x < 2 1 2 ≤ x It doesn’t provide explicitly the range of X . It doesn’t matter here! Probability mass function at each point = change of cumulative distribution function. In this example, the cumulative distribution function only changes at X =- 2 , and 2. So essentially the range of X is {- 2 , , 2 } . (Because at other points P ( X ) = 0.) Andrew Liu CDF, Mean, and Variance of Discrete Random Variables Cumulative Distribution Function – Examples E.g. 1. (Textbook Example 3-7) Determine the probability mass function of X from the following cumulative distribution function. F ( x ) = x <- 2 . 2- 2 ≤ x < . 7 0 ≤ x < 2 1 2 ≤ x It doesn’t provide explicitly the range of X . It doesn’t matter here! Probability mass function at each point = change of cumulative distribution function. In this example, the cumulative distribution function only changes at X =- 2 , and 2. So essentially the range of X is {- 2 , , 2 } ....
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HW sol - CDF Mean and Variance of Discrete Random Variables...

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