11.7. Summary

Try these first

1. 1.

   Define a raw moment.

   Hint

   Think of moments calculated about the origin.

2. 2.

   What does the first central moment measure?

   Hint

   Consider how deviations from the mean behave.

3. 3.

   What is the first central moment?

   • E[X]
   • 0
   • E[(X-μ)^2]

   Hint

   Think about the definition of deviation from the mean.

4. 4.

   If MGFs exist for random variables, they uniquely determine their distributions.

   • True
   • False

   Hint

   Remember what MGFs do for distributions.

5. 5.

   Given a discrete random variable with a specific distribution, compute its first four moments using the definitions.

   Hint

   Use the definition of moments learned earlier.

6. 6.

   Show how MGFs can simplify finding variances for two independent random variables.

   Hint

   Remember the additivity property of MGFs!