Finding expected value for a poisson random variable?

I am given the PDF of a uniform random variable with the parameter of A, f(x)= 1/A where t is an element of (0,a) and 0 everywhere else.

My teacher says the number of people arriving in interval (0,s] is viewed as a poisson random variable with the parameter of sB, and Y is the number of people arriving while one of them is being served. I'm told to find the expected value for a random variable, Y.

Would the expected value of this problem be the sum from 0 to s of f(x)?

As in f(0) + f(1) + ... + f(s)= answer?

I am a little confused as to how this works!

Re: Finding expected value for a poisson random variable?

Hey elpermic.

If you are looking at some fixed interval and all intervals are independent and stationary then the mean for that interval is just the mean of the Poisson Process for that interval.

Re: Finding expected value for a poisson random variable?

So in short it is just the sum of f(x) from intervals 0 to s? Or would it be from 0 to a?

As in my answer would be 0 + 1 + 1/2 + ... + 1/s?