Students arrive for the much dreaded JEE Advanced according to a Poisson process with rate lambda. For the sanitization process, they must stand in a queue, each student can take a different time or the same time compared with some other student for sanitization. Let us denote the time taken by ii the student as Xi. Xi is independent identically distributed random variables. We assume that Xi takes integer values in range 1,2, …, n, with probabilities p1, p2, …, pn . Find the PMF for Nt, the number of students in the sanitization queue at time t.
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