SOCR EduMaterials Activities Poisson Distribution - Revision history

Jenny: Reverted edit of EvkWtl, changed back to last version by IvoDinov

2007-08-17T22:47:24Z

Reverted edit of EvkWtl, changed back to last version by IvoDinov

EvkWtl at 00:44, 17 August 2007

2007-08-17T00:44:22Z

IvoDinov at 17:26, 6 August 2007

2007-08-06T17:26:12Z

IvoDinov at 17:25, 6 August 2007

2007-08-06T17:25:41Z

Nchristo: /* This is an activity to explore the Poisson Probability Distribution. */

2006-12-29T00:46:55Z

‎This is an activity to explore the Poisson Probability Distribution.

IvoDinov at 00:30, 29 December 2006

2006-12-29T00:30:49Z

New page

== 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 <math> \lambda=2 </math>. What is the shape of this distribution?

* '''Exercise 2:''' Use SOCR to graph and print the distribution of a Poisson random variable with <math> \lambda=15 </math>. What is the shape of this distribution? What happens when you keep increasing <math> \lambda </math>?

* '''Exercise 3:''' Let <math> X \sim Poisson(5) </math>. Find <math> P(3 \le X < 10) </math>, and <math> P(X >10 | X \ge 4) </math>.

* '''Exercise 4:''' Poisson approximation to binomial: Graph and print <math> X \sim b(60, 0.02) </math>. Approximate this probability distribution using Poisson. Choose three values of <math> X </math> 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 <math> \lambda=5 </math>. In this graph you can also see the probability that between 2 and 5 events will occur.

<center>[[Image: SOCR_Activities_Christou_poisson.jpg|600px]]</center>

<hr>
* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals}}

</math>

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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.==
+== 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 .
@@ Line 22: / Line 22: @@
 ** What is the probability that at least 4 people enter the casino during that time?
-* '''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>
+* '''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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-== This is an activity to explore the Poisson Probability 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.==
 * '''Description''':  You can access the applets for the above distributions at  http://www.socr.ucla.edu/htmls/SOCR_Distributions.html .
@@ Line 22: / Line 22: @@
 ** What is the probability that at least 4 people enter the casino during that time?
-* '''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>
+* '''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>

@@ Line 20: / Line 20: @@
 * '''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?
+** What is the probability that at least 4 people enter the casino during that time?
 * '''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>

← Older revision		Revision as of 17:25, 6 August 2007
Line 14:		Line 14:

	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.
−

	<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?
		+
		+	* '''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>

@@ Line 24: / Line 24: @@
 * SOCR Home page: http://www.socr.ucla.edu
-{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals}}
+{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_Poisson_Distribution}}
 </math>