11. Partial Differential Equations

Try these first

1. 1.

   Define raw moment and give an example.

   Hint

   Think about the expected values.

2. 2.

   What does variance measure?

   Hint

   Consider how values deviate from the average.

3. 3.

   What is the first moment known as?

   • Skewness
   • Variance
   • Mean

   Hint

   Think about what the average value represents.

4. 4.

   True or False: The second central moment is equal to the variance.

   • True
   • False

   Hint

   Remember how variance is defined.

5. 5.

   Given a random variable X with MGF M_X(t) = e^{(μ + σ^2 t^2)/2}, find the first and second moments.

   Hint

   Remember that the first moment is the first derivative evaluated at t=0.

6. 6.

   Calculate the variance from a given MGF, M_X(t) if its derivatives provide moments: M'_X(0) = 2, M''_X(0) = 6.

   Hint

   Use the relationship between variance and moments.