Let X X2 Xn be iid r vs from Normalmu sigma Show that the rv

Let X,. X2 ,Xn be i,i,d, r. v.\'s from Normal(mu, sigma). Show that the r.v. K = n sigma i-1 (x1 - mu / sigma)^2 has a chi-square distribution with degrees of freedom n. Show that (n-1)s^2 / sigma^2 = n sigma i-1 (Xi - mu / sigma)^2 - (X - mu / sigma / squareroot n)^2. What is the distribution of (n - 1)S^2 / sigma^2 ? Simply X - mu / sigma / squareroot n / squareroot[(n-1)S^2 / sigma^2] / (n - 1). What is the distribution of X - mu / S / squareroot n ? Find the probability of P(-t a/2

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