Poisson Probability Calculator

Answer:

$ P(4) $ Probability of exactly 4 occurrences: 0.16803135574154


Solution:

$P(4)$ Probability of exactly 4 occurrences

If using a calculator, you can enter $ \lambda = 3 $ and $ x = 4 $ into a poisson probability distribution function (PDF). If doing this by hand, apply the poisson probability formula: $$ P(x) = \frac{{e^{-\lambda}} \cdot {\lambda^x}}{x!} $$ where $x$ is the number of occurrences, $\lambda$ is the mean number of occurrences, and $e$ is the constant 2.718. Substituting in values for this problem, $ x = 4 $ and $ \lambda = 3 $, we have $$ P(4) = \frac{{e^{-3}} \cdot {3^4}}{4!} $$ Evaluating the expression, we have $$ P(4) = 0.16803135574154 $$