MATH370: Statistical Theory I

Course Description

Objectives

1. Model events occurring in nature in mathematical notation for future study.
   
   
2. Acquaint students with how to describe populations and predict events when only samples are available.
   
   
3. Illustrate how industry uses statistical models in the design and production of goods and services.
   
   
4. Develop an appreciation for the use of mathematical concepts such as calculus in the development of statistics.
   
   
5. Acquaint students with the rather short history of statistics, its recent growth in applications, and current development.

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Grading Procedure

Attendance Policy

Course Outline

• Chapter 1: Introduction (1 class day)

  Brief history, some examples
  
  

• Chapter 2: Probability (8 days)

  Sample spaces, Events, Counting sample points, Probability of an event, Additive rules, Conditional probability, Multiplicative rules, Bayes. rule.
  
  

• Chapter 3: Random Variables and Probability Distributions (8 days)

  Random variable, Discrete probability distributions, Continuous probability distributions, Empirical distributions, Joint probability distributions.
  
  

• Chapter 4: Mathematical Expectation (8 days)

  Mean of a random variable, Variance and covariance, Means and variances of linear combinations of random variables, Chebyshev.s theorem.
  
  

• Chapter 5: Some Discrete Distributions (10 days)

  Discrete uniform distribution, Binomial and multinomial distributions, Hypergeometric distribution, Negative binomial and geometric distributions, Poisson distribution and the Poisson process.
  
  

• Chapter 6: Some Continuous Probability Distributions (10 days)

  Continuous probability distribution, Normal distribution, Areas under the normal curve, Applications of the normal distribution, Normal approximation of the binomial distribution, Gamma and exponential distributions, Applications of the gamma and exponential distributions, Chi-Squared distribution, Lognormal distribution, Weibull distribution.
  
  
• Note: At appropriate places in this course, time should be allotted to elaborate on the historical aspects relevant to the subject.