Let X1, X2, X3, …, Xn be a random sample from N(mu, sigma^2) distribution and S^2 = 1/n-1sumi=1^n(Xi-barX)^2, barX=1/nsumi=1^nXi. What is the moment-generating function of S^2?

Q2Section I (Objective (Q1–Q80))2 of 79

Distribution Theory — moment generating function of sample variance

Let $X_1, X_2, X_3, …, X_n$ be a random sample from $N(\mu, \sigma^2)$ distribution and $S^2 = \frac{1}{n-1}\sum_{i=1}^{n}(X_i-\bar{X})^2$ , $\bar{X}=\frac{1}{n}\sum_{i=1}^{n}X_i$ . What is the moment-generating function of $S^2$ ?

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