# 11. In this question, we will explore the motivation for equation (21.37). Let X1,…,Xn ~ N(0, s2).

11. In this question, we will explore the motivation for equation (21.37). Let X1,…,Xn ~ N(0, s2). Let s = vn × median (|X1|,…, |Xn|) 0.6745 . (a) Show that E(s ) = s. (b) Simulate n = 100 observations from a N(0,1) distribution. Compute s as well as the usual estimate of s. Repeat 1,000 times and compare the MSE. (c) Repeat (b) but add some outliers to the data. To do this, simulate each observation from a N(0,1) with probability .95 and simulate each observation from a N(0,10) with probability .95