Let {N(t) : t >=0} be a Poisson process of rate 1 and let denote the times of the points. Derive the pdf of

So I've been trying to work with the distribution function. I have:

I get stuck there though and can't find a similar example.

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- December 13th 2010, 03:13 AMBeakypoisson process
Let {N(t) : t >=0} be a Poisson process of rate 1 and let denote the times of the points. Derive the pdf of

So I've been trying to work with the distribution function. I have:

I get stuck there though and can't find a similar example. - December 13th 2010, 06:29 AMFocus
- December 13th 2010, 11:08 AMBeaky
Sorry, typo in original post. It's . I'll try to use your advice anyways though.

- December 13th 2010, 12:45 PMBeaky
I get to

But I get stuck here. I can't figure out how to apply conditioning and the law of total probability since the variables are continuous. - December 13th 2010, 03:48 PMFocus