SOCR EduMaterials FunctorActivities MGF Moments

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 $X \sim Binomial(10,.5)$
- b. Find the Expected Value of $X \sim Normal(0,1)$
- c. Find the Expected Value of $X \sim ChiSquare(13)$

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 $1 s t$ Moment. If we take the second derivative of the MGF with respect to t, where $t = 0$ . We get $E (X 2)$ . 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 $3 r d$ and <math<4^{th}</math> derivatives of a MGF and set $t = 0$ ?

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