19 Activity 1

The purpose of this activity is to refresh your memory on some basic properties of probability distributions that you learned about in mathematical statistics (e.g., STAT 610 or STAT 770 at KSU). The secondary purpose of this activity is to assess your computational skills.

You are encouraged to work with others students in the class to complete this activity.

Make sure to show all of your work and computer code, so that your mathematical and numerical results are easily reproducible. In the most basic sense, this is equivalent to “showing your work” as you would with pencil and paper in a mathematics course.

  1. Take 500 draws from a normal distribution that has an expected value of 2 and a variance of 9. Make a histogram of these 500 draws.

  2. Calculate the sample mean from the 500 draws from problem 1.

  3. Take 500 draws from Bernoulli distribution that has an expected value of 0.5. Make a histogram of these 500 draws.

  4. Calculate the sample mean from the 500 draws from problem 3.

  5. Take 500 draws from Bernoulli distribution that has a variance of 0.25.

  6. Take 500 draws from a normal distribution that has an expected value of 0 and a variance of 1. Raise these 500 draws to the second power and make a histogram.

  7. What well-known and named probability density function is shown in the histogram you made in question 6?

  8. Take 500 draws from a a normal distribution that has an expected value of 0 and a variance of 1. If a draw is greater than zero, set it to the value one. If a draw is less than zero set it zero. Make a histogram of these 500 draws that are zero or one.

  9. What well-known and named probability mass function is shown in the histogram you made in question 8? What is the expected value and variance of this probability mass function?