SOCR EduMaterials FunctorActivities Bernoulli Distributions - Revision history

IvoDinov: /* See also */

2008-01-09T06:28:04Z

‎See also

IvoDinov at 06:27, 9 January 2008

2008-01-09T06:27:47Z

Rgidwani at 03:02, 9 January 2008

2008-01-09T03:02:35Z

Rgidwani at 03:02, 9 January 2008

2008-01-09T03:02:05Z

Rgidwani at 02:54, 9 January 2008

2008-01-09T02:54:06Z

Rgidwani at 02:51, 9 January 2008

2008-01-09T02:51:38Z

Rgidwani at 02:48, 9 January 2008

2008-01-09T02:48:13Z

Rgidwani at 02:44, 9 January 2008

2008-01-09T02:44:29Z

Rgidwani at 02:29, 9 January 2008

2008-01-09T02:29:57Z

Rgidwani at 02:28, 9 January 2008

2008-01-09T02:28:11Z

@@ Line 24: / Line 24: @@
 ==See also==
-* [[SOCR_EduMaterials_FunctorActivities_MGF | Other SOCR Distribution FUnctor Activities]]
+* [[SOCR_EduMaterials_FunctorActivities_MGF | Other SOCR Distribution Functor Activities]]
 <hr>

← Older revision		Revision as of 06:27, 9 January 2008
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	* '''Exercise 4:''' Graph the PDF and the MGF for the appropriate Distribution where <math> M_x(t)={({3 \over 4}e^t+{1\over 4})}^{15} </math>. Be sure to include the correct parameters for this distribution, for example if <math> X \sim Geometric(p) </math> be sure to include the numeric value for <math>p</math>		* '''Exercise 4:''' Graph the PDF and the MGF for the appropriate Distribution where <math> M_x(t)={({3 \over 4}e^t+{1\over 4})}^{15} </math>. Be sure to include the correct parameters for this distribution, for example if <math> X \sim Geometric(p) </math> be sure to include the numeric value for <math>p</math>
		+
		+	==See also==
		+	* [[SOCR_EduMaterials_FunctorActivities_MGF \| Other SOCR Distribution FUnctor Activities]]
		+
		+	<hr>
		+	* SOCR Home page: http://www.socr.ucla.edu
		+
		+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_FunctorActivities_Bernoulli_Distributions}}

← Older revision		Revision as of 03:02, 9 January 2008
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	**c. How does this relate to Exercise 1? Does having the same MGF mean they are distributed the same?		**c. How does this relate to Exercise 1? Does having the same MGF mean they are distributed the same?

−	* '''Exercise 4:''' Graph the PDF and the MGF for the appropriate Distribution where <math> M_x(t)={({3 \over 4}e^t+{1\over 4})}^{15} </math>. Be sure to include the correct parameters for this distribution, for example if <math> X \sim Geometric(p) </math> be sure to include the numeric value for </math>p</math>	+	* '''Exercise 4:''' Graph the PDF and the MGF for the appropriate Distribution where <math> M_x(t)={({3 \over 4}e^t+{1\over 4})}^{15} </math>. Be sure to include the correct parameters for this distribution, for example if <math> X \sim Geometric(p) </math> be sure to include the numeric value for <math>p</math>

@@ Line 17: / Line 17: @@
 * '''Exercise 3:''' You learned in class about the properties of MGF's If <math> X_1, ...X_n</math> are iid. and <math>Y = \sum_{i=1}^n X_i. </math> then <math>M_{y}(t) = {[M_{X_1}(t)]}^n</math>.
-**a. Show that the MGF of the sum of n independent Bernoulli Trials with success probability <math> p </math> is the same as the MGF of the Binomial Distribution using the corollary above.
+**a. Show that the MGF of the sum of <math>n</math> independent Bernoulli Trials with success probability <math> p </math> is the same as the MGF of the Binomial Distribution using the corollary above.
-**b. Show that the MGF of the sum of n independent Geometric Random Variables with success probability <math> p </math> is the same as the MGF of the Negative-Binomial Distribution using the corollary above.
+**b. Show that the MGF of the sum of <math>n</math> independent Geometric Random Variables with success probability <math> p </math> is the same as the MGF of the Negative-Binomial Distribution using the corollary above.
-**c.  How does this relate to Exercise 1?
+**c.  How does this relate to Exercise 1?  Does having the same MGF mean they are distributed the same?

@@ Line 17: / Line 17: @@
 * '''Exercise 3:''' You learned in class about the properties of MGF's If <math> X_1, ...X_n</math> are iid. and <math>Y = \sum_{i=1}^n X_i. </math> then <math>M_{y}(t) = {[M_{X_1}(t)]}^n</math>.
-**a. Show that the MGF of the sum of n independent Bernoulli Trials with success probability <math> p </math> is the same as the MGF of the Binomial Distribution using the corollar above.
+**a. Show that the MGF of the sum of n independent Bernoulli Trials with success probability <math> p </math> is the same as the MGF of the Binomial Distribution using the corollary above.
-**b. Show that the MGF of the sum of n independent Geometric
+**b. Show that the MGF of the sum of n independent Geometric Random Variables with success probability <math> p </math> is the same as the MGF of the Negative-Binomial Distribution using the corollary above.

← Older revision		Revision as of 02:51, 9 January 2008
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	* '''Exercise 3:''' You learned in class about the properties of MGF's If <math> X_1, ...X_n</math> are iid. and <math>Y = \sum_{i=1}^n X_i. </math> then <math>M_{y}(t) = {[M_{X_1}(t)]}^n</math>.		* '''Exercise 3:''' You learned in class about the properties of MGF's If <math> X_1, ...X_n</math> are iid. and <math>Y = \sum_{i=1}^n X_i. </math> then <math>M_{y}(t) = {[M_{X_1}(t)]}^n</math>.
		+	**a. Show that the MGF of the sum of n independent Bernoulli Trials with success probability <math> p </math> is the same as the MGF of the Binomial Distribution using the corollar above.
		+	**b. Show that the MGF of the sum of n independent Geometric

← Older revision		Revision as of 02:48, 9 January 2008
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	* '''Exercise 2:''' Use SOCR to graph and print the MGF of the distribution of a geometric random variable with <math> p=0.2, p=0.7 </math>. What is the shape of this function? What happens when <math> p </math> is large? What happens when <math> p </math> is small?		* '''Exercise 2:''' Use SOCR to graph and print the MGF of the distribution of a geometric random variable with <math> p=0.2, p=0.7 </math>. What is the shape of this function? What happens when <math> p </math> is large? What happens when <math> p </math> is small?

−	* '''Exercise 3:''' You learned in class about the properties of MGF's If <math> X_1, ...X_n are iid. and Y = \sum_{i=1}^n X_i. </math> then	+	* '''Exercise 3:''' You learned in class about the properties of MGF's If <math> X_1, ...X_n</math> are iid. and <math>Y = \sum_{i=1}^n X_i. </math> then <math>M_{y}(t) = {[M_{X_1}(t)]}^n</math>.

← Older revision		Revision as of 02:44, 9 January 2008
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	<center>[[Image:BernoulliMGF.jpg\|600px]]</center>		<center>[[Image:BernoulliMGF.jpg\|600px]]</center>

		+	Do you notice any similarities between the graphs of these MGF's between any of these distributions?

−	~~Do you notice any similarities between~~ the ~~graphs~~ of ~~these~~ MGF's ~~between any of these distributions?~~	+	* '''Exercise 2:''' Use SOCR to graph and print the MGF of the distribution of a geometric random variable with <math> p=0.2, p=0.7 </math>. What is the shape of this function? What happens when <math> p </math> is large? What happens when <math> p </math> is small?
		+
		+	* '''Exercise 3:''' You learned in class about the properties of MGF's If <math> X_1, ...X_n are iid. and Y = \sum_{i=1}^n X_i. </math> then

@@ Line 10: / Line 10: @@
 Below you can see a snapshot of the MGF of the distribution of <math> X \sim Bernoulli(0.8) </math>
-[[Image:BernoulliMGF.jpg]]
+<center>[[Image:BernoulliMGF.jpg|600px]]</center>
 Do you notice any similarities between the graphs of these MGF's between any of these distributions?

@@ Line 5: / Line 5: @@
 * '''Exercise 1:''' Use SOCR to graph the MGF's 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 Bernoulli(0.5) </math>
-**b.<math> x \sim Binomial(1,0.5) </math>
+**b.<math> X \sim Binomial(1,0.5) </math>
-**c.<math> x \sim Geometric(0.5) </math>
+**c.<math> X \sim Geometric(0.5) </math>
-**d.<math> x \sim NegativeBinomial(1, 0.5) </math>
+**d.<math> X \sim NegativeBinomial(1, 0.5) </math>
 Below you can see a snapshot of the MGF of the distribution of <math> X \sim Bernoulli(0.8) </math>
-[[Image:Example.jpg]]
+[[Image:BernoulliMGF.jpg]]
 Do you notice any similarities between the graphs of these MGF's between any of these distributions?