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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
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