# Thread: Poisson Distribution Question: Probability, Mean and Variance

1. ## Poisson Distribution Question: Probability, Mean and Variance

Just Slow Down is a public awareness campaign in Winnipeg to help drivers understand the relationship of excessive speed to traffic collisions, injuries, and fatalities. On their website, it says " On average, there are 35 collisions each day on Winnipeg streets. It should come as no surprise that two thirds of collisions occur at intersections".

c) Find the probability that the number of collisions will be more than four in a randomly selected day.

P(x > 4) = 1-P(x less than or equal to 4) = 1-P(x=0)-P(X=1)-P(x=2)-P(x=3)-P(x=4)

I used the mean to be 35 and I ended up with

P(x > 4) = 1- 6.3051E-16 - 2.2068E-14 - 3.8619E-13 - 4.5055E-12 - 3.9423E-11

I tried putting this into my calculator but cant seem to find an answer. I dont know if i did the whole thing wrong or if im not putting it into my calculator right?

d) Find the mean and variance of the number of collisions on a given week in winnipeg.

With a poisson distribution, the mean and variance is mu, µ. But over a week i dont know what to do. Would you just add 35 7 times?

Any help will be appreciated.

2. ## Re: Poisson Distribution Question: Probability, Mean and Variance

Why do you mean when you say you can't seem to find an answer?

For the second part - do you know what distribution of the sum of independent poisson random variables is?

3. ## Re: Poisson Distribution Question: Probability, Mean and Variance

I tried entering it in and i would get a different answer like 1 or a negative number that didnt seem like the right probability ill try again and no i do not know what that is for the second part

4. ## Re: Poisson Distribution Question: Probability, Mean and Variance

Well the calculator giving an answer of 1 is fairly reasonable. The answer *basically* is 1.

5. ## Re: Poisson Distribution Question: Probability, Mean and Variance

If you are having trouble with your calculator try googling

1- 6.3051E-16 - 2.2068E-14 - 3.8619E-13 - 4.5055E-12 - 3.9423E-11

6. ## The Following User Says Thank You to asterisk For This Useful Post:

Trae88 (10-27-2013)

7. ## Re: Poisson Distribution Question: Probability, Mean and Variance

So if the probability is 1 than it means that there will always be more than 4 collisions per day?

8. ## Re: Poisson Distribution Question: Probability, Mean and Variance

Well the probability isn't *exactly* 1. But it's really really close.

9. ## Re: Poisson Distribution Question: Probability, Mean and Variance

Ah okay i get it and about the distribution of the sum of independent poisson random variable I looked it up but i dont really understand it nor how to apply it. I have not learned about this yet in university.

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