# Show that (a) Show that E(X - ) = 0, 2 = E(X 2 ) - 2 . (b) Prove (10)-(12). (c) Find all the moments of the uniform distribution on an interval x b. (d) The skewness of a random variable X is defined by Show that for a symmetric distribution (whose third

Chapter 24, PROBLEM SET 24.6 #20

Show that

(a) Show that E(X - μ) = 0, σ2 = E(X2) - μ2.

(b) Prove (10)-(12).

(c) Find all the moments of the uniform distribution on an interval α x b.

(d) The skewness ϒ of a random variable X is defined by

Show that for a symmetric distribution (whose third central moment exists) the skewness is zero.

(e) Find the skewness of the distribution with density f(x) = xe-x when x > 0 and f(x) = 0 otherwise. Sketch f(x).

(f) Find a nonsymmetric discrete distribution with 3 possible values, mean 0, and skewness 0.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...

## This problem has been solved!

Related Book For

10th edition

Authors: Erwin Kreyszig

ISBN: 978-0470458365