## STAT414 probability theory课程简介

STAT 414 is an introductory course in probability theory, which covers the fundamental concepts, theorems, and applications of probability. The course aims to provide students with a solid foundation in probability theory, including both theoretical and practical aspects of the subject.

The three main goals of the course are:

1. To learn the theorems of basic probability: The course covers the fundamental theorems of probability, including the axioms of probability, conditional probability, Bayes’ theorem, independence, random variables, and probability distributions.
2. To learn applications and methods of basic probability: The course also covers various applications of probability theory, including counting techniques, discrete and continuous probability distributions, and limit theorems. Students will learn how to use these methods to solve real-world problems.
3. To develop theoretical problem-solving skills: The course emphasizes the development of theoretical problem-solving skills, including the ability to understand and use mathematical proofs, and to reason logically and rigorously about probability concepts. Students will be challenged to solve theoretical problems and to apply their understanding of probability to solve practical problems.

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## PREREQUISITES

The three main goals of the course are:

1. To learn the theorems of basic probability: The course covers the fundamental theorems of probability, including the axioms of probability, conditional probability, Bayes’ theorem, independence, random variables, and probability distributions.
2. To learn applications and methods of basic probability: The course also covers various applications of probability theory, including counting techniques, discrete and continuous probability distributions, and limit theorems. Students will learn how to use these methods to solve real-world problems.
3. To develop theoretical problem-solving skills: The course emphasizes the development of theoretical problem-solving skills, including the ability to understand and use mathematical proofs, and to reason logically and rigorously about probability concepts. Students will be challenged to solve theoretical problems and to apply their understanding of probability to solve practical problems.

## STAT414 probability theory HELP（EXAM HELP， ONLINE TUTOR）

1. Give examples of how probability applies to each of the following areas.
(a) Lottery draws
(b) Public opinion polls
(c) Sending data over a network
(d) Auditing of expense items in a financial statement
(e) Disease transmission (e.g. measles, tuberculosis, STD’s)

(a) Lottery draws: Probability is used to determine the chances of winning a particular lottery draw. For example, the probability of winning the Mega Millions lottery jackpot is 1 in 302,575,350.

(b) Public opinion polls: Probability is used to estimate the proportion of a population that holds a particular opinion. Pollsters use random sampling methods to select a representative sample of the population and then use probability calculations to estimate the margin of error and the confidence level of their results.

(c) Sending data over a network: Probability is used to ensure that data packets are transmitted reliably and without errors. Error detection and correction algorithms use probability calculations to determine the likelihood of a transmission error and to correct errors when they occur.

(d) Auditing of expense items in a financial statement: Probability is used to determine the likelihood of errors or fraudulent transactions in a financial statement. Auditors use statistical sampling methods to select a sample of transactions to examine and then use probability calculations to determine the likelihood that errors or fraud exist in the entire population of transactions.

(e) Disease transmission (e.g. measles, tuberculosis, STD’s): Probability is used to estimate the likelihood of disease transmission within a population. Epidemiologists use mathematical models that take into account factors such as the infectiousness of the disease, the size and demographics of the population, and the effectiveness of preventive measures such as vaccination to estimate the risk of transmission and to develop strategies for controlling outbreaks.

1. Which of the following can be accurately described by a “deterministic” model, that is, a model which does not require any concept of probability?
(a) The position of a small particle in space
(b) The velocity of an object dropped from the leaning tower of Pisa
(c) The lifetime of a heavy smoker

## Textbooks

• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.

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