24 Assignment 1

Due 11:59pm Sunday January 22

The purpose of this assignment 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 assignment is to assess your computational skills.

You must complete this assignment individually, however, you may participate in a learning group of any size to complete the assignment, but please submit your own work (i.e., do not copy another person’s work).

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.

Please save the file as a pdf and name it Yourlastname_Assignment1. Upload this file to Canvas.

  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.