Let X1, X2, ..., Xnbe a random sample from population having probability density function f(xi) =

1

√2πσ2

e−(

1

2σ

2 (xi−µ)2), −∞ < xi < ∞

(i) Using the characteristic function technique, determine the distribution of

Y =

n

X

i=1

Xi2

(ii) Using the moment generating function technique, determine the distribution of

the sample mean X