MATH 4261 Introduction to Mathematical Statistics

Fall 2003

Professor Spruill

Course Materials

• CDL students.
• Grading.
• Compare your grades with those of the class
  • inclass/homework (score is 5 times online quiz total plus the scores on the homeworks).
  • exam 1
• Homework problem assignments.
• Quizonline .
• Coverage of topics for Exam I.
• Coverage of topics for the Final Exam.
• Due dates
• Exams and selected solutions .

• Standard probability distributions
• Reproductive properties and linear combinations.
• Some standard confidence intervals.
• Some standard hypothesis tests.
• SAS Proc TTest program, data, and output.

• Simulations

  • Simulate Poisson process paths.
  • An MM1 queue has Poisson arrivals and exponential service times. Simulate this process in which you choose the arrival rate and service time distribution.
  • In class we proved mathematically that the square of a standard normal rand om variable has a chi-square distribution with one degree of freedom. Empirical evidence of this c an be obtained here. Simulate Maple 4 , Maple 5 , Maple 7 n standard normal random variables, forming a histogram of their squares, and plotting on the same axis the chi-square 1 density. You can try different values of n. For n a thousand or so you'll observe a pretty close correspondence.
  • Simulate Maple4 , Maple 5, Maple 7 an instance of the central limit theorem.