Find the cumulative distribution function, Civil Engineering

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Find the Cumulative Distribution Function:

Find the cdf of Y = Z² where Z ^-N (0,l)

Solution:

F(y)= P(Y ≤ y) = p(z²≤y) = P(-√y≤ √z≤√y)

= ?(√y)- ?(-√y) = ?(√y) - (1 - ?√y)

Hence

F(Y) = [2 ?(√y)-l]

where ? ( z ) is the cdf of Z.

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