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 6.6. Find the probability that the next two months will both result in four accidents each occurring on this stretch of road.
A) 0.011568
B) 0.107553
C) 0.215105
D) 0.002341

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ accidents in a month, when accidents follow a Poisson distribution with mean $\lambda$, is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$. Here, $\lambda = 6.6$ and $k = 4$. So, for one month, $P(X=4) = \frac{e^{-6.6} 6.6^4}{4!}$. Since the number of accidents in each month is independent, the probability of observing 4 accidents in both months is the product of the probabilities for each month: $P(X=4)^2 = \left(\frac{e^{-6.6} 6.6^4}{4!}\right)^2 \approx 0.011568$.