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.

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:...