The moment-generating function of the random variable X

Last updated: 7/11/2022

The moment-generating function of the random variable X having a chi-squared distribution with v degrees of freedom is My(t) = (1-2t)^-v/2 show that the mean and variance of the chi-squared distribution with v degrees of freedom are, respectively, v and 2v. This moment about the origin can be found by evaluating For any value of L, the derivative identified in the previous step is Evaluating this expression at (Simplify your answers.) The variance of X, o, is given by the expression yields v. Thus, the mean of the chi-squared distribution with v degrees of freedom is The first term of this expression can be found by evaluating For any value of t, the derivative identified in the previous step is Use this moment-generating function to