Poisson distribution

The Poisson Distribution is an approximation to the Binomial Distribution.

Recall:
•

P(x)= {_n}C_{x}\;p^x(1-p)^{n-x}

n

: number of trials

x

: number of success in n trials

p

: probability of success in each trial

P(x)

: probability of getting x successes (out of n trials)
•

\mu=np

Now:
•

\mu=\lambda=np

Poisson Distribution:

P(x)=e^{-\lambda}

\frac{\lambda^x}{x!}

• poissonpdf

(\lambda,x)

• poissoncdf

(\lambda,x)

1.
Determining the Poisson Distribution
The number of meteors that hit the earth in a given day is modelled by a Poisson Distribution with $\lambda=4$ . What is the probability that 5 meteors hit the earth in a day?

2.
When making a video I typically make 1 error for every 20 minutes of video time. If I make 45 minutes of video what is the probability that I make 3 errors?

4.
Cumulative Poisson Distribution
On U.S. route 66 (an American highway) every car that travels this whole route has a probability of $p=0.0002$ of getting into a car accident. A total of 10,000 cars drive this route every month. What is the probability that there are fewer than 3 car accidents in a month?