- #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?