SOCR EduMaterials FunctorActivities MGF Moments - Revision history

IvoDinov at 06:29, 9 January 2008

2008-01-09T06:29:22Z

Rgidwani at 03:31, 9 January 2008

2008-01-09T03:31:18Z

Rgidwani at 03:28, 9 January 2008

2008-01-09T03:28:40Z

Rgidwani: New page: == This is an activity to explore useful properties of MGF's.== * '''Description''': You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_Distri...

2008-01-09T03:11:48Z

New page: == This is an activity to explore useful properties of MGF's.== * '''Description''': You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_Distri...

New page

== This is an activity to explore useful properties of MGF's.==

* '''Description''': You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_DistributionFunctors.html .

← Older revision		Revision as of 06:29, 9 January 2008
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	* '''Exercise 4:''' What do we get when we take the <math>3^{rd}</math> and <math<4^{th}</math> derivatives of a MGF and set <math> t=0 </math>?		* '''Exercise 4:''' What do we get when we take the <math>3^{rd}</math> and <math<4^{th}</math> derivatives of a MGF and set <math> t=0 </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_MGF_Moments}}

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 * '''Exercise 2:''' Can you use MGF's to find the Expected Value for the Continuous Uniform Distribution?  Why or why not?
-* '''Exercise 3:'''  In Exercise 1, we calculated the 1^{st} Moment.  If we take the second derivative of the MGF with respect to t, where <math> t=0 </math>.  We get <math> E(X^2) </math>.  We can use this to find the Variance of a particular Distribution.  Repeat Parts (a,b,c) for Exercise 1, but this time calculate the variance.
+* '''Exercise 3:'''  In Exercise 1, we calculated the <math>1^{st}</math> Moment.  If we take the second derivative of the MGF with respect to t, where <math> t=0 </math>.  We get <math> E(X^2) </math>.  We can use this to find the Variance of a particular Distribution.  Repeat Parts (a,b,c) for Exercise 1, but this time calculate the variance.
-* '''Exercise 4:'''  What do we get when we take the 3^{rd} and 4^{th} derivatives of a MGF and set <math> t=0 </math>?
+* '''Exercise 4:'''  What do we get when we take the <math>3^{rd}</math> and <math<4^{th}</math> derivatives of a MGF and set <math> t=0 </math>?

← Older revision		Revision as of 03:28, 9 January 2008
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	* '''Description''': You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_DistributionFunctors.html .		* '''Description''': You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_DistributionFunctors.html .
		+
		+	* '''Exercise 1:''' As you have learned in class, there are quite a few interesting properties that Moment Generating Functions hold. For example you learned that <math> E(X^n)=M_{x}^{(n)}(0)={d^n M_x(t)\over{dt^n}}\mid_{t=0} </math> If the MGF is defined in the neighborhood of 0. So to get the Expected Value for a particular distribution, you would take the first derivative of the MGF and set t=0. Use SOCR to graph and print the following distributions and answer the questions below. ''You must do these exercises using MGF's, you can find the slope using the mouse pointer.''
		+	**a. Find the Expected Value of <math> X \sim Binomial(10,.5) </math>
		+	**b. Find the Expected Value of <math> X \sim Normal(0,1) </math>
		+	**c. Find the Expected Value of <math> X \sim ChiSquare(13) </math>
		+
		+	* '''Exercise 2:''' Can you use MGF's to find the Expected Value for the Continuous Uniform Distribution? Why or why not?
		+
		+	* '''Exercise 3:''' In Exercise 1, we calculated the 1^{st} Moment. If we take the second derivative of the MGF with respect to t, where <math> t=0 </math>. We get <math> E(X^2) </math>. We can use this to find the Variance of a particular Distribution. Repeat Parts (a,b,c) for Exercise 1, but this time calculate the variance.
		+
		+	* '''Exercise 4:''' What do we get when we take the 3^{rd} and 4^{th} derivatives of a MGF and set <math> t=0 </math>?