- #1

Of Mike and Men

- 54

- 3

## Homework Statement

Accidents at a busy intersection follow a Poisson distribution with three accidents expected in a week.

What is the probability that at least 10 days pass between accidents?

## Homework Equations

F(X) = 1- e

^{-λx}

μ = 1/λ

## The Attempt at a Solution

Let x = amount of time between accidents in days

My r.v. is continuous so x~Exponential(λ=?)

E(x) = 3/7 (in days)

Since E(x) = μ = 1/λ = 3/7

λ = 7/3

Thus x~Exponential(λ=7/3)

P(X≥10) = 1-P(X≤10) = 1- F(10) = 1- e

^{-70/3}

Answer in the back of the book says:

λ = 3/7

P(X≥10) = 1-P(X≤10) = 1- F(10) = 1- e

^{-30/7}

I'm confused why λ = 3/7 and not 7/3 if my expected value is 3/7. Shouldn't lambda, by definition, be its reciprocal?