GATE 2013 CS (CS1) – Question 12
Cars per minute at a junction between 5 PM and 6 PM follow a Poisson distribution with mean three. Find the probability of fewer than three cars in a minute.
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Correct answer: (C) $17/(2e^3)$
Explanation
For X∼Poisson(3), $P(X<3)=e^{-3}(1+3+3^2/2!)=e^{-3}(17/2)=17/(2e^3)$. Thus C. Fewer than three includes counts zero, one and two.