Lecture 1

Lecturer Information

• Lecturer: Do Duc Tan

• Email: tan.dd@vgu.edu.vn

• Office: Academic Cluster 1, Room 211

• Office Hours: By appointments

Course Overview

Course Description

• Introduction to Probability Theory and Statistics

• Explores concepts of chance and uncertainty

• Provides foundation for statistical inference through experimentation and data analysis

• Relevant in a quantitative world

Assessment Criteria

• Attendance: 10%

• Tutorials: 30%, includes 15 tutorials

• Exam: 60%, date will be announced

• Retake Policy: Available for students receiving either a Fail or Pass grade

Academic Honesty

• Cheating and plagiarism considered serious offenses

• Consequences include failing the course

• Refer to Syllabus for more details

Lecture Content

Key Topics

• Probability: experiments, outcomes, sample spaces, Venn diagrams, probability values

Introduction to Probability

• Probability as a mathematical branch handling chance and uncertainty

• Basis for statistical inference via experiments and data analysis

Sample Spaces and Experiments

Definition of an Experiment

• Experiment: A process producing outcomes

• Sample Space (S): All possible outcomes of an experiment

Example 1: Machine Breakdowns

• Sample space S = {electrical, mechanical, misuse}

• Uncertainty in breakdown causes

Example 2: Defective Computer Chips

• Sample space S = {0 defectives, 1 defective, ..., 500 defectives}

Example 3: Power Plants

• Supervised by a manager; each can be generating (1) or idle (0)

• Sample space: S = {(0,0,0),(1,0,0),(0,1,0),(0,0,1),(1,1,0),(1,0,1),(0,1,1),(1,1,1)}

Games of Chance

Coin Tossing

• Sample space for single toss: S = {head, tail}

• Sample space for two tosses: S = {(head, head), (head, tail), (tail, head), (tail, tail)}

Die Rolling

• Sample space for a single die: S = {1, 2, 3, 4, 5, 6}

• When two dice are rolled, consider all combinations for outcomes

Card Playing

• Sample space from a standard deck of 52 cards

Drawing with Replacement

• Sample space comprises 2704 combinations

• Specific outcome like (A♡, A♡) is possible

Drawing without Replacement

• Total outcomes reduce to 2652; outcomes like (A♡, A♡) are not possible

Probability Values

Definition and Properties

• Probability values assigned to elements of sample space

• Conditions: 0 ≤ p1, p2, ..., pn ≤ 1 and p1 + p2 + ... + pn = 1

Example 4: Machine Breakdowns (Probability Assignment)

• P(electrical) = 0.2, P(mechanical) = 0.5, P(misuse) = 0.3

• Interpretation of probabilities indicates likelihood of breakdown reasons

Estimating Probability Assignments

• Derived from collection of data and prior experiences

Probability of Outcomes in Games of Chance

Coin Tossing

• Fair coin: P(head) = P(tail) = 0.5

• Biased coin example with p = 0.4

Die Rolling

• Fair die, all outcomes equally likely: P(1) = P(2) = ... = P(6) = 1/6

Drawing Cards

• Initial card drawn has 52 outcomes, P = 1/52

• If drawn with replacement, each outcome still equally likely

• Without replacement alters total outcomes affecting probability distribution