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!