Compute Probabilities of a Poisson Random Variable
-The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.2. Find the probability of observing exactly three accidents on this stretch of road next month.
A) 0.025239
B) 4.575166
C) 0.374135
D) 67.820284

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ accidents when the events follow a Poisson distribution with mean $\lambda$ is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$. For $\lambda = 8.2$ and $k = 3$, $P(X=3) = \frac{e^{-8.2} * 8.2^3}{3!}$, which calculates to approximately 0.025239.