Find the value of c when n 5 n 6 graph c as a function of

Question

Let X₁, X₂, ..... , X_n be a random sample of size I/ from a normal distribution.

(a) Show that an unbiased estimator for σ is cS, where

c = [√(n - 1) τ{(n - 1) / 2} / √2 τ(n/2)]

HINT: Recall that the distribution of (n - 1)S² / σ² χ² (n - 1)_.

(b) Find the value of c when n = 5, n = 6.

(c) Graph c as a function of n. What is the limit of c as n increases without bound?