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There is a poisson process N with rate $\lambda$. $T_1$ and $T_2$ are the first and second arrival times.

How do you calculate $$P(T_1 \le t_1 , T_2 \le t_2 , N_t=2) $$

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    So you can write $\{N_t=2\}$ as $\{T_2 That would allow you to write $P(T_1 \le t_1 , T_2 \le t_1 , T_2. Still not sure how to procede2012-10-21
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    I'm pretty sure you need to use the inter-arrival times and the fact that they are independent.2012-10-21

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