# stochastic process

1. ### Poisson process: phone calls

We assume that phone calls arrive according to a Poisson process with rate 2. If I know that up to time t = 1 there is one call only, how likely is it that it arrived after t = 0.75? If I know that up to time t = 1 two calls arrived, how likely is it that the second arrived after t = 0.75? So...
2. ### How to evaluate Mean and Variance of Min Function??

Detail is Given in Image attach
3. ### customer service problem

N customers circulate in a closed system with two servers. In Server 1 and Server 2, service times are exponential with parameters µ1 and µ2, respectively. Let state K denotes that there are k customers in Stage 1(thus N-k customers in stage 2). I'd like to determine P(K), which is the...
4. ### stochastic process distribution vs. distributions of subcollections

Hello, I am looking for a reason why the following would be true: Suppose Y = { Y_t : t = 0, +- 1, +- 2, ... } is a stochastic process. The probability distribution of the stochastic process Y is completely determined by the set of all joint probability distributions of finite...