The Poisson distribution with parameter lambda = .3 has been assigned for the outcome of an experiment. Let X be the outcome function. Find P(X = 0), P(X = 1), and P(X > 1)

In general, the Poisson distribution is \(P(X = k) \approx \frac{\lambda^k}{k!}e^{-\lambda}\). We’re given \(\lambda = .3\), so all we need is to substitute k for the appropriate X.

\(P(X = 0) = \frac{.3^0}{0!}e^{-.3} = e^{-.3} \approx 0.7408\)

\(P(X = 1) = \frac{.3^1}{1!}e^{-.3} = .3e^{-.3} \approx .2222\)

\(P(X > 1) = 1 - (P(X = 0) + P(X = 1)) \approx 0.0369\)

pX0 <- exp(-.3)
pX1 <- .3 * exp(-.3)
pXgreater1 <- 1 - (pX0 + pX1)

pX0
## [1] 0.7408182
pX1
## [1] 0.2222455
pXgreater1
## [1] 0.03693631