Exercise 6. (10 points) Let X1,X2,,Xn be mutually independent and identically distributed
random variables with means and variance 2. Let X=(i=1nXi)/n. Show that
k=1n(XkX)2=k=1n(Xk)2n(X)2 and hence E[k=1n(XkX)2]=(n1)2.
Exercise 6. (10 points) Let X1,X2,�,Xn be mutually independent and id.pdf
1. Exercise 6. (10 points) Let X1,X2,,Xn be mutually independent and identically distributed
random variables with means and variance 2. Let X=(i=1nXi)/n. Show that
k=1n(XkX)2=k=1n(Xk)2n(X)2 and hence E[k=1n(XkX)2]=(n1)2