Question

In a Poisson distribution, μ = 3.80. (Round your answers to 4 decimal places.)

1. What is the probability that x = 2?

2. What is the probability that x > 2?

Answer 1

a)

Here, λ = 3.8 and x = 2
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 2)
P(X = 2) = 3.8^2 * e^-3.8/2!
P(X = 2) = 0.1615
Ans: 0.1615

b)

Here, λ = 3.8 and x = 2
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > 2) = 1 - P(X <= 2).
P(X > 2) = 1 - (3.8^0 * e^-3.8/0!) + (3.8^1 * e^-3.8/1!) + (3.8^2 * e^-3.8/2!)
P(X > 2) = 1 - (0.0224 + 0.085 + 0.1615)
P(X > 2) = 1 - 0.2689 = 0.7311