11.1.2.1. Raw Moments (or Moments about the Origin)

Try these first

1. 1.

   Define a raw moment.

   Hint

   Think of it as a way to quantify how a random variable behaves.

2. 2.

   What is the first raw moment?

   Hint

   Recall what average means in the context of random variables.

3. 3.

   What is the raw moment of a random variable?

   • Expected value of deviations
   • Expected value of powers
   • Average of a distribution

   Hint

   Focus on the definition of raw moments.

4. 4.

   True or False: The first central moment is always equal to the mean.

   • True
   • False

   Hint

   Think about the relationship between mean and central moments.

5. 5.

   Given a continuous random variable with a known probability density function, derive the first four moments using integrating techniques.

   Hint

   Think about using integration by parts for higher moments if needed.

6. 6.

   Analyze a dataset with statistical software to extract raw moments and compare them to central moments to illustrate their relationships.

   Hint

   Make sure to observe the formulas linking these moments.