SOCR EduMaterials Activities Poisson Distribution

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[http://saibso.org/uruguay-fiume.htm uruguay (fiume)] [http://kinunia.cn/mp-cruzer.htm mp3 cruzer] == This is an activity to explore the Poisson Probability Distribution.==
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== 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 .  
* '''Description''':  You can access the applets for the above distributions at  http://www.socr.ucla.edu/htmls/SOCR_Distributions.html .  
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** What is the probability that at least 4 people enter the casino during that time?
** 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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* '''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>

Revision as of 22:39, 17 August 2007

This is an activity to explore the Poisson Probability Distribution.


  • 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  X \sim Poisson(5) . Find  P(3 \le X < 10) , and  P(X >10 | X \ge 4) .
  • Exercise 4: Poisson approximation to binomial: Graph and print  X \sim b(60, 0.02) . 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 X1 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 λ1 = 5 is a reasonable model for X1. Now, let X2 denote the number of vehicles passing a point on the westbound lane of the same highway in 1 hour. Suppose that X2 has a Poisson distribution with mean λ2 = 3. Of interest is Y = X1 + X2, the total traffic count in both lanes in one hour. What is the P(Y < 5)?





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