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## Homework Statement

The rate of occurrence of events in a non-homogeneous Poisson process is given by: λ(t)=12t e

^{-2t}.

(c) Find the p.d.f. of the time until the first event occurs after time t = 1.

(e) After what time is it 95% certain that no further events will occur?

## Homework Equations

λ(t)=12t e

^{-2t}

## The Attempt at a Solution

After using integration by parts, I found μ(t) = -3e

^{-2t}(2t+1) to solve other parts of this question. I know part (e) requires the use of newton-raphson method but I have no idea how to go about. Any help will really be appreciated, thanks.

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