Allied & ICAR Exam Bank • ALLIED_2746 NAT • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Poisson, normal and binomial distributions

Question Statement:

For a Poisson process with arrival rate $\lambda = 2$ events per hour, the probability of zero arrivals in one hour is $e^{-k}$. The integer $k$ is:

Answer Key:

2

Step-by-Step Solution & Explanation

$P(X = 0) = \frac{e^{-\lambda} \lambda^0}{0!} = e^{-2}$. Hence $k = 2$.
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