Students arrive for the much dreaded JEE Advanced according to a Poisson process with rate lambda. For sanitization process they must stand in a queue,each student can take different time or same time compared with some other student for sanitization. Let us denote the time taken by ith student as Xi . Xi are 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 sanitization queue at time t.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Students arrive for the much dreaded JEE Advanced according to a Poisson process with rate lambda. For sanitization process they must stand in a queue,each student can take different time or same time compared with some other student for sanitization. Let us denote the time taken by ith student as Xi .
Xi are 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 sanitization queue at time t.

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