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

for k ≥ 1. (Note that this equality would be equivalent to the equality in Chebyshev’s inequality if the variance of W were equal to 1.) Then the cdf satisfies

Also, the symmetry assumption implies that

(a) Show that the pdf of W is

(b) Find the mean and the variance of W and interpret your results.

(c) Graph the cdf of W.

ST 701 Week Five Notes MaLyn Lawhorn September 12, 2017 and September 14, 2017 Last Time ▯ Cumulative Distribution Function (CDF) – denoted X (x) – gives the probability that X ▯ x, x 2 R – Properties: 1. non-decreasing function 2. F(▯1) = 0, F(+1) = 1 3. right-continuousX F (x)...