Chapter 5, Question 13, Page 199

13 The Poisson distribution with parameter λ = .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).

Answer

\(P(X=x)=(e^{\lambda})*((\lambda^{x})/x!)\)

We can use dpois() function to find the exact probability of \(P(X=0)\) and \(P(X=1)\)

dpois(x=0, lambda =0.3)
## [1] 0.7408182
dpois(x=1, lambda =0.3)
## [1] 0.2222455

We can use ppois() function to find the probability of \(P(X>1)\)

ppois(q=1, lambda = 0.3, lower.tail = TRUE)
## [1] 0.9630637