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# Suppose that W is a continuous random variable with mean 0 and a symmetric pdf f(w) and

ISBN: 9780321923271 41

## Solution for problem 5.8-7 Chapter 5.8

Probability and Statistical Inference | 9th Edition

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Problem 5.8-7

Suppose that W is a continuous random variable with mean 0 and a symmetric pdf f(w) and cdf F(w), but for which the variance is not specified (and may not exist). Suppose further that W is such that P(|W 0| < k) = 1 1 k2 for k 1. (Note that this equality would be equivalent to the equality in Chebyshevs inequality if the variance of W were equal to 1.) Then the cdf satisfies F(w) F(w) = 1 1 w2 , w 1. Also, the symmetry assumption implies that F(w) = 1 F(w). (a) Show that the pdf of W is f(w) = 1 |w| 3 , |w| > 1, 0, |w| 1. (b) Find the mean and the variance of W and interpret your results. (c) Graph the cdf of W.

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Week one Lecture #1 Chapter 3- Section 3.3 What is Statistics- Statistics is the branch of mathematics that deals with the collections Population vs. Sample Population: entire group of entities that we want information about Sample: Part of the population that we actually examine in order to gather info Census:...

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##### ISBN: 9780321923271

This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. The answer to “Suppose that W is a continuous random variable with mean 0 and a symmetric pdf f(w) and cdf F(w), but for which the variance is not specified (and may not exist). Suppose further that W is such that P(|W 0| < k) = 1 1 k2 for k 1. (Note that this equality would be equivalent to the equality in Chebyshevs inequality if the variance of W were equal to 1.) Then the cdf satisfies F(w) F(w) = 1 1 w2 , w 1. Also, the symmetry assumption implies that F(w) = 1 F(w). (a) Show that the pdf of W is f(w) = 1 |w| 3 , |w| > 1, 0, |w| 1. (b) Find the mean and the variance of W and interpret your results. (c) Graph the cdf of W.” is broken down into a number of easy to follow steps, and 133 words. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This full solution covers the following key subjects: . This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Since the solution to 5.8-7 from 5.8 chapter was answered, more than 243 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 5.8-7 from chapter: 5.8 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM.

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