SOCR EduMaterials Activities Binomial Distributions - Revision history

Nchristo: /* This is an activity to explore the Binomial, Geometric, and Hypergeometric Probability Distributions. */

2009-10-15T05:26:27Z

‎This is an activity to explore the Binomial, Geometric, and Hypergeometric Probability Distributions.

IvoDinov at 20:23, 17 May 2007

2007-05-17T20:23:40Z

Nchristo: /* This is an activity to explore the Binomial, Geometric, and Hypergeometric Probability Distributions. */

2007-02-06T04:18:33Z

‎This is an activity to explore the Binomial, Geometric, and Hypergeometric Probability Distributions.

IvoDinov at 00:34, 29 December 2006

2006-12-29T00:34:54Z

New page

== This is an activity to explore the Binomial, Geometric, and Hypergeometric Probability Distributions.==

* '''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 following distributions and answer the questions below. Also, comment on the shape of each one of these distributions:
**a. <math> X \sim b(10,0.5) </math>, find <math> P(X=3) </math>, <math> E(X) </math>, <math> sd(X) </math>, and verify them with the formulas discussed in class.
**b. <math> X \sim b(10,0.1) </math>, find <math> P(1 \le X \le 3) </math>.
**c. <math> X \sim b(10,0.9) </math>, find <math> P(5 < X < 8), \ P(X < 8), \ P(X \le 7), \ P(X \ge 9) </math>.
**d. <math> X \sim b(30,0.1) </math>, find <math> P(X > 2) </math>.

Below you can see a snapshot of the distribution of <math> X \sim b(20,0.3) </math>

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

* '''Exercise 2:''' Use SOCR to graph and print the distribution of a geometric random variable with <math> p=0.2, p=0.7 </math>. What is the shape of these distributions? What happens when <math> p </math> is large? What happens when <math> p </math> is small?

Below you can see a snapshot of the distribution of <math> X \sim geometric(0.4) </math>

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

* '''Exercise 3:''' Select the geometric probability distribution with <math> p=0.2 </math>. Use SOCR to compute the following:
**a. <math> P(X=5) </math>
**b. <math> P(X > 3) </math>
**c. <math> P(X \le 5) </math>
**d. <math> P(X > 6) </math>
**e. <math> P(X \ge 8) </math>
**f. <math> P(4 \le X \le 9) </math>
**g. <math> P(4 < X < 9) </math>

* '''Exercise 4:''' Verify that your answers in exercise 3agree with the formulas discussed in class, for example, <math> P(X=x)=(1-p)^{x-1}p </math>, <math> P(X > k)=(1-p)^k </math>, etc. Write all your answers in detail using those formulas.

* '''Exercise 5:''' Let <math> X </math> follow the hypergeometric probability distribution with <math> N=52 </math>, <math> n=10 </math>, and number of "hot" items 13. Use SOCR to graph and print this distribution.

Below you can see a snapshot of the distribution of <math> X \sim hypergeometric(N=100, n=15, r=30) </math>

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

* '''Exercise 6:''' Refer to exercise 5. Use SOCR to compute <math> P(X=5) </math> and write down the formula that gives this answer.

* '''Exericise 7:''' Binomial approximation to hypergeometric: Let <math> X </math> follow the hypergeometric probability distribution with <math> N=1000, \ n=10 </math> and number of "hot" items 50. Graph and print this distribution.

* '''Exercise 8:''' Refer to exerciise 7. Use SOCR to compute the exact probability: <math> P(X=2) </math>. Approximate <math> P(X=2) </math> using the binomial distribution. Is the approximation good? Why?

* '''Exercise 9:''' Do you think you can approximate well the hypergeometric probability distribution with <math> N=50, \ n=10 </math>, and number of "hot" items 40 using the binomial probability distribution? Explain.

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

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← Older revision		Revision as of 05:26, 15 October 2009
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	* '''Exercise 8:''' Refer to exercise 7. Use SOCR to compute the exact probability: <math> P(X=2) </math>. Approximate <math> P(X=2) </math> using the binomial distribution. Is the approximation good? Why?		* '''Exercise 8:''' Refer to exercise 7. Use SOCR to compute the exact probability: <math> P(X=2) </math>. Approximate <math> P(X=2) </math> using the binomial distribution. Is the approximation good? Why?

−	* '''Exercise 9:''' Do you think you can approximate well the hypergeometric probability distribution with <math> N=50, \ n=10 </math>, and number of "hot" items 40 using the binomial probability distribution? ~~Explain~~.	+	* '''Exercise 9:''' Do you think you can approximate well the hypergeometric probability distribution with <math> N=50, \ n=20 </math>, and number of "hot" items 40 using the binomial probability distribution? Graph and print the exact (hypergeometric) and the approximate (binomial) distributions and compare.

@@ Line 44: / Line 44: @@
 * '''Exercise 6:''' Refer to exercise 5.  Use SOCR to compute <math> P(X=5) </math> and write down the formula that gives this answer.
-* '''Exericise 7:''' Binomial approximation to hypergeometric:  Let <math> X </math> follow the hypergeometric probability distribution with <math> N=1000, \ n=10 </math> and number of "hot" items 50.  Graph and print this distribution.
+* '''Exercise 7:''' Binomial approximation to hypergeometric:  Let <math> X </math> follow the hypergeometric probability distribution with <math> N=1000, \ n=10 </math> and number of "hot" items 50.  Graph and print this distribution.
-* '''Exercise 8:''' Refer to exerciise 7.  Use SOCR to compute the exact probability: <math> P(X=2) </math>.  Approximate <math> P(X=2) </math> using the binomial distribution.  Is the approximation good?  Why?
+* '''Exercise 8:''' Refer to exercise 7.  Use SOCR to compute the exact probability: <math> P(X=2) </math>.  Approximate <math> P(X=2) </math> using the binomial distribution.  Is the approximation good?  Why?
 * '''Exercise 9:''' Do you think you can approximate well the hypergeometric probability distribution with <math> N=50, \ n=10 </math>, and number of "hot" items 40 using the binomial probability distribution?  Explain.

@@ Line 32: / Line 32: @@
 **g. <math> P(4 < X < 9) </math>
-* '''Exercise 4:''' Verify that your answers in exercise 3agree with the formulas discussed in class, for example, <math> P(X=x)=(1-p)^{x-1}p </math>, <math> P(X > k)=(1-p)^k </math>, etc.  Write all your answers in detail using those formulas.
+* '''Exercise 4:''' Verify that your answers in exercise 3 agree with the formulas discussed in class, for example, <math> P(X=x)=(1-p)^{x-1}p </math>, <math> P(X > k)=(1-p)^k </math>, etc.  Write all your answers in detail using those formulas.
 * '''Exercise 5:''' Let <math> X </math> follow the hypergeometric probability distribution with <math> N=52 </math>, <math> n=10 </math>, and number of "hot" items 13.  Use SOCR to graph and print this distribution.