SOCR EduMaterials FunctorActivities MGF Moments
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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>? | ||
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+ | ==See also== | ||
+ | * [[SOCR_EduMaterials_FunctorActivities_MGF | Other SOCR Distribution Functor Activities]] | ||
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+ | <hr> | ||
+ | * SOCR Home page: http://www.socr.ucla.edu | ||
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+ | {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_FunctorActivities_MGF_Moments}} |
Current revision as of 06:23, 9 January 2008
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 .
- 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 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
- b. Find the Expected Value of
- c. Find the Expected Value of
- 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 1st Moment. If we take the second derivative of the MGF with respect to t, where t = 0. We get E(X2). 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 3rd and <math<4^{th}</math> derivatives of a MGF and set t = 0?
See also
- SOCR Home page: http://www.socr.ucla.edu
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