Question

Suppose X ~ N(0,1).

a.) Derive the expression of cdf F(x) for X^2

b.) Find the numerical value of F(2)

Answer 1

Let X be a random variable which follows N(0,1). Then the probability density function of X is given by

For N(0,1) the PDF is given by

​​​​​​Let us consider another random variable Y, then the P(Y<y)=F(y) gives the cdf of Y given by .

b) For y=2, the numberical value of F(2) is obtained by

However it is not easy to manually calculate above value one can use r software for the numberical finding of the above value.