# Statistics I: Probability Theory & Statistical Inference (505)

# Course Objectives

The objectives of the course are to introduce the underlying concepts of probability
and statistical inference.
In particular, this course will provide a foundation in the underlying probability
theory and distribution theory required
for application of statistical inference. This theory will be built upon in
STAT06 and other later courses. It is expected that
students will have a solid prerequisite foundation calculus before enrolling
in this course.

Topics: We will cover exploratory data analysis, probability theory, conditional
probability, independence, Bayes’ theorem,
discrete distributions (binomial, hypergeometric, geometric, negative binomial,
Poisson), moment generating functions,
continuous distributions (uniform, exponential, gamma, normal), mixed distributions,
bivariate and multivariate distributions.
In addition, we will cover sampling distribution theory, correlation, linear
functions of random variables and introduce the Central Limit Theorem.

# Tentative Schedule of Weekly Topics

1 Basic Concepts, Numerical Characteristics, Probability Set Functions

2 Properties of Probability, Methods of Enumeration

3 Random Variables, Probability Density Functions

4 Distribution Functions, Mathematical Expectation

5 Special Mathematical Expectations, Chebyshev’s Inequality

6 Correlation, Correlation Coefficient, Stochastic Independence

7 Discrete Random Variables: binomial, multinomial, and Poisson distributions

8 Continuous Random Variables: Gamma, Chi-Square, and Beta distributions

9 Continuous Random Variables: Normal and Bivariate Normal distributions

10 Sampling Theory, Transformations of Random Variables

11 The t and F distributions, Order Statistics,

12 Moment Generating Function Technique, distribution of the sample mean and
variance

13 Limiting Distributions, Stochastic Convergence

14 Limiting Moment Generating Functions

15 Central Limit Theorem