# Poisson distribution. E(X) not a whole number.

1. Sep 28, 2013

### Darth Frodo

1. The problem statement, all variables and given/known data
During the day, cars pass along a point on a remote road at an average rate of one per 20 minutes.

Calculate the probability that;

(i) in the course of an hour no car passes;
(ii) in the course of 30 minutes exactly 4 cars pass;

2. Relevant equations

$P(X = x) = \frac{e^{-\lambda}\lambda^{x}}{x!}$

3. The attempt at a solution

$\lambda = 3$

$P(X = 0) = e^{-3} = 0.0497$

My question: In part 2 $\lambda = 1.5$. Can $\lambda$ be a Real number or must it be an integer? I assume it can be any number as $E(X)$ does not necessarily have to be in the support of X.

Thanks.

2. Sep 28, 2013

### Staff: Mentor

λ can be any non-negative real number.