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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- Dec 13th 2010, 02:13 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. - Dec 13th 2010, 05:29 AMFocus
- Dec 13th 2010, 10:08 AMBeaky
Sorry, typo in original post. It's . I'll try to use your advice anyways though.

- Dec 13th 2010, 11:45 AMBeaky
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. - Dec 13th 2010, 02:48 PMFocus