11.3.2.1. Existence

Try these first

1. 1.

   Define a moment in your own words.

   Hint

   Think about its significance in describing data.

2. 2.

   What is the first raw moment?

   Hint

   Consider what average represents.

3. 3.

   What does the first raw moment measure?

   • Variance
   • Mean
   • Skewness

   Hint

   Consider what average signifies.

4. 4.

   True or False: A central moment can be negative.

   • True
   • False

   Hint

   Think about the definition of variance.

5. 5.

   Given a random variable with certain probabilities, determine the first four moments and explain their significance.

   Hint

   Apply both raw and central moment formulas.

6. 6.

   Using an MGF, derive the expected value and variance, then use a real-world application to explain.

   Hint

   Relate your findings back to applications in finance or engineering.