Discussion 7

5.1 Question 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).

\[Poisson~Distribution~=P(X = k) = \lambda^ke^{-\lambda}/k!\]

1. P(X = 0)

lambda <- 0.3
k <- 0
X0 <- lambda**k * exp(-lambda)/factorial(k)
round(X0, 4)

## [1] 0.7408

2. P(X = 1)

lambda <- 0.3
k <- 1
X1 <- lambda**k * exp(-lambda)/factorial(k)
round(X1, 4)

## [1] 0.2222

3. P(X = 2)

lambda <- 0.3
k <- 2
X2 <- lambda**k * exp(-lambda)/factorial(k)
round(X2, 4)

## [1] 0.0333