SOCR EduMaterials Activities Poisson Distribution
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Below you can see the distribution of a Poisson random variable with <math> \lambda=5 </math>. In this graph you can also see the probability that between 2 and 5 events will occur. | Below you can see the distribution of a Poisson random variable with <math> \lambda=5 </math>. In this graph you can also see the probability that between 2 and 5 events will occur. | ||
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<center>[[Image: SOCR_Activities_Christou_poisson.jpg|600px]]</center> | <center>[[Image: SOCR_Activities_Christou_poisson.jpg|600px]]</center> | ||
+ | * '''Exercise 5:''' People enter a gambling casino at a rate of 1 for every two minutes. | ||
+ | ** What is the probability that no one enters between 12:00 and 12:05? | ||
+ | ** What is the probability that at least 4 people enter the casino during that time? | ||
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+ | * '''Exercise 6:''' Let <math>X_1</math> denote the number of vehicles passing a particular point on the eastbound lane of a highway in 1 hour. Suppose that the Poisson distribution with mean <math>\lambda_1=5</math> is a reasonable model for <math>X_1</math>. Now, let <math>X_2</math> denote the number of vehicles passing a point on the westbound lane of the same highway in 1 hour. Suppose that <math>X_2</math> has a Poisson distribution with mean <math>\lambda_2= 3</math>. Of interest is <math>Y= X_1 + X_2</math>, the total traffic count in both lanes in one hour. What is the <math>P(Y < 5) ?</math> | ||
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* SOCR Home page: http://www.socr.ucla.edu | * SOCR Home page: http://www.socr.ucla.edu | ||
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Current revision as of 16:51, 11 December 2013
This is an activity to explore the Poisson Probability Distribution.
- Description: You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_Distributions.html .
- Exercise 1: Use SOCR to graph and print the distribution of a Poisson random variable with λ = 2. What is the shape of this distribution?
- Exercise 2: Use SOCR to graph and print the distribution of a Poisson random variable with λ = 15. What is the shape of this distribution? What happens when you keep increasing λ?
- Exercise 3: Let . Find , and .
- Exercise 4: Poisson approximation to binomial: Graph and print . Approximate this probability distribution using Poisson. Choose three values of X and compute the probability for each one using Poisson and then using binomial. How good is the approximation?
Below you can see the distribution of a Poisson random variable with λ = 5. In this graph you can also see the probability that between 2 and 5 events will occur.
- Exercise 5: People enter a gambling casino at a rate of 1 for every two minutes.
- What is the probability that no one enters between 12:00 and 12:05?
- What is the probability that at least 4 people enter the casino during that time?
- Exercise 6: Let X_{1} denote the number of vehicles passing a particular point on the eastbound lane of a highway in 1 hour. Suppose that the Poisson distribution with mean λ_{1} = 5 is a reasonable model for X_{1}. Now, let X_{2} denote the number of vehicles passing a point on the westbound lane of the same highway in 1 hour. Suppose that X_{2} has a Poisson distribution with mean λ_{2} = 3. Of interest is Y = X_{1} + X_{2}, the total traffic count in both lanes in one hour. What is the P(Y < 5)?
- SOCR Home page: http://www.socr.ucla.edu
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