Consider a sequence of i.i.d. r.v.'s

Z_(1),dots,Z_(n)

where each

Z_(i)N(0,1)

.\ (a) Write down the relationship between the

Z_(i)

's and

W

, where

W\\\\chi _(n-1)^(2)

\ (b) Now consider another sequence of i.i.d. r.v.'s

x_(1),dots,x_(n)

where each

x_(i)N(\\\\mu ,\\\\sigma ^(2))

\ and let\

S^(2)=(\\\\sum_(i=1)^n (x_(i)-(\\\\bar{x} ))^(2))/(n-1)

\ (i)Write down the relationship between

S^(2)

and

W

.

Consider a sequence of i.i.d. r.v.'s Z1,,Zn where each ZiN(0,1). 3 (a) Write down the relationship between the Zi 's and W, where Wn12 (b) Now consider another sequence of i.i.d. r.v.'s X1,,Xn where each XiN(,2) and let S2=n1i=1n(XiX)2 (i)Write down the relationship between S2 and W. Consider a sequence of i.i.d. r.v.'s Z1,,Zn where each ZiN(0,1). 3 (a) Write down the relationship between the Zi 's and W, where Wn12 (b) Now consider another sequence of i.i.d. r.v.'s X1,,Xn where each XiN(,2) and let S2=n1i=1n(XiX)2 (i)Write down the relationship between S2 and W