GATE | GATE CS 2013 | Question 2

Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?
(A) 8 / (2e3)
(B) 9 / (2e3)
(C) 17 / (2e3)
(D) 26 / (2e3)


Answer: (C)

Explanation: See http://en.wikipedia.org/wiki/Poisson_distribution#Definition

PR(X < 3) = Pr(x = 0) + Pr(x = 1) + Pr(x = 2) = f(0, 3) + f(1, 3) + f(2, 3) Put \lambda = 3 and k = 0, 1, 2 in the formula given at http://en.wikipedia.org/wiki/Poisson_distribution#Definition
= 17 / (2e3)



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