Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t$ $\lambda = 0.8 , t = 3 , P ( 2 )$
A) 0.0431
B) 0.2613
C) 0.9569
D) 0.3840

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a Poisson distribution is given by the formula $P(k; \lambda t) = \frac{e^{-\lambda t}(\lambda t)^k}{k!}$. For this problem, $\lambda = 0.8$, $t = 3$, and $k = 2$. Plugging these values into the formula gives $P(2) = \frac{e^{-2.4}(2.4)^2}{2!} = 0.2613$.

Determine the Indicated Probability for a Poisson Random Variable with the Given