Find the Cumulative Distribution Function:
Find the cdf of Y = Z^{2} where Z ^{-}N (0,l)
Solution:
F(y)= P(Y ≤ y) = p(z^{2}≤y) = P(-√y≤ √z≤√y)
= ?(√y)- ?(-√y) = ?(√y) - (1 - ?√y)
Hence
F(Y) = [2 ?(√y)-l]
where ? ( z ) is the cdf of Z.