The course will introduce the basic notion of probability theory and its application to statistics. The focus will be on the discussion of applications.

The text that will be used is:

R.V. Hoggs and E.A. Tanis "Probability ans Statistical Inference",
8th edition

The syllabus can be found here.

There will be two midterm.

The exercise listed are for HW collection. I will collect them every two weeks and grade 2 or 3 exercises among the one assigned. In case of differences between the 8th and 7th editions of the book I will indicate in square brackets the number relative to the 7th edition.

The final grade will be based on the following rules: 45% final, 35% midterms, 20% HW. Curving will be done on the final result.

**First Midterm: **February
18 Second Midterm: March
25

- Axioms, Interpretations and Properties of Probabilities
- Probability Distributions for Discrete Random Variables
- Example of Discrete Random Variables
- Continuous Random Variables and Probability Density Functions
- Example of Continuous Random Variables
- The central limit theorem
- Jointly Distributed Random Variables
- Point Estimation
- Statistical Intervals
- Test of Hypotheses
- Simple Linear Regression (time permitting)

**First week**

Material covered:

- General Introduction

- 1.1 Basic Concepts

- 1.2 Properties of Probability

Exercises:

- (1.1) 2, 7

- (1.2) 6, 15, 19

Material covered:

- 1.3 Methods of Enumeration

- 1.4 Conditional Probability
- 1.5 Independent Events

Exercises:

- (1.3) 7, 11

- (1.4) 1, 10, 15

- (1.5) 3, 18, 19

Material covered:

- 1.6 Bayes's Theorem

- 2.1 Random Variable of Discrete Type

Exercises:

- (1.6) 4, 8, 11

- (2.1) 3, 7, 17

Fourth week

Material covered:

- 2.2 Mathematical Expectation

- 2.3 The Mean, Variance and Standard Devioayion
- 2.4 Bernoulli Trials and the Binomial Distribution

Exercises:

- (2.2) 5, 12

- (2.3) 5, 13, 19

- (2.4) 7, 22

Material covered:

- 2.5 The Moment-Generating Function

- 2.6 The Poisson Distribution

Exercises:

- (2.5) 3, 11, 21

- (2.6) 13, 15, 21

Material covered:

- 3.1 Continuous-Type Data
- 3.2 Exploratory Data Analysis

Exercises:

- (3.1) 3, 10, 12

- (3.2) 4, 9

The first midterm will be on Tuesday February 25. It will cover Chapter 1 and 2 complete plus section 3.1 and 3.2 from the book.

Preparation Material

- Test and solution set.
- Test and solution set.
- Test and solution set.
- Test and solution set.
- Test and solution set

Third HW collection on Teusday March 11th.

Material covered:

- 3.3 Random Variable of Continuous Type

- 3.4 The Uniform and Exponential Distribution

Exercises:

- (3.3) 2, 7, 23

- (3.4) 5, 6, 14, 20

Material covered:

- 3.5 The Gamma and Chi-square Distributions

- 3.6 The Normal Distribution

Exercises:

- (3.5) 8, 11

- (3.6) 5, 7, 14, 25

Material covered:

- 4.1 Distributions of 2 Random Variables

- 4.2 The Correlation Coefficient
- 4.3 Conditional Distributions
- 4.4 The Bivariate Normal Distribution

Exercises:

- (4.1) 5, 12, 15

- (4.2) 1, 7, 10

- (4.3) 6. 16

- (4.4) 8

Fourth HW collection on Teusday April 1st.

Preparation material for the second
midterm:

- Test and solution set.
- Test and solution set.
- Test and solution set.
- Test and solution set.
- Test and solution set

Material covered:

- 5.1 Functions of One Random Variable

- 5.3 Several Independent Random Variables

- 5.6 The Central Limit Theorem

Exercises:

- (5.1) 6, 8

- (5.3) 6, 11, 22

- (5.6) 7, 8, 12

Material covered:

- 6.1 Point Estimation

- 6.2 Confidence Interval for the Mean

Exercises:

- (6.1) 5, 13, 15

- (6.2) 5, 10, 14

Last HW collection on Thursday April 17.

Take home midterm due on April 22.