11.1.3. Important Moments

Try these first

1. 1.

   Define a moment in your own words.

   Hint

   What does it help us understand about a graph?

2. 2.

   What is the first moment and what does it signify?

   Hint

   What is an average?

3. 3.

   What is the first moment also known as?

   • Mean
   • Variance
   • Kurtosis

   Hint

   It's what you often find as the average.

4. 4.

   The variance measures what aspect of a distribution?

   • Asymmetry
   • Spread
   • Peakedness

   Hint

   Think about how tight or loose the data is around the average.

5. 5.

   A certain dataset has its second raw moment equal to 20 and the first moment equal to 5. Calculate the variance from these values.

   Hint

   Remember the variance formula and consider interpreting the results.

6. 6.

   If the MGF of a random variable is given as M(t) = e^(2t + t^2), find the variance.

   Hint

   Differentiate the MGF stepwise to derive moments at t=0.