# Question: Prove that all odd central moments of a Gaussian random

Prove that all odd central moments of a Gaussian random variable are equal to zero. Furthermore, develop an expression for all even central moments of a Gaussian random variable.

## Answer to relevant Questions

Show that the variance of a Cauchy random variable is undefined (infinite). A random variable has a CDF given by (a) Find the mean of X; (b) Find the variance of X; (c) Find the coefficient of skewness of X; (d) Find the coefficient of kurtosis of X. Consider a Gaussian random variable, X, with mean µ and variance σ2. (a) Find E [X|X > u + σ] (b) Find E [X|| X –u| < σ] In each of the following cases, find the value of the parameter a which causes the indicated random variable to have a mean value of 10. (a) (b) (c) A pair of random variables, (X, Y), is equally likely to fall anywhere within the region defined by |X| + |Y| ≤ 1. (a) Write the form of the joint PDF, fX,Y (x,y). (b) Find the marginal PDFs, fX (x) and fY (y). (c) Find ...Post your question