An Integral Proof of the Joint M.G.F. of Sample Mean and Variance

Without assuming independence of sample mean and variance, or without using any conditional distribution, we present an integral proof of the joint moment generating function for sample mean and variance for independently, identically and normally distributed random variables. This proves the independence of sample mean and variance which is the basis of Student t-Test and many other inferential methods. IJSS, Vol. 24(2)s (Special Issue), December, 2024, pp 19-23