Problem 9E

Find the distribution of W = X2 when

(a) X is N(0, 4),

(b) X is N(0, σ2).

Answer :

Step 1 of 3 :

A random variable X is normally distributed with mean and standard deviation .

The probability density function is

f(x) =

The claim is to find the distribution of w = when.

- X ~ N(0, 4)

- X ~ N(0, )

In general, ~ with one degrees of freedom.

Where, v =

The probability density function of v is

P( V v) = dy , 0 < v <

= dy