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Probability for Actuaries

Introduction to Discrete Distribution

Gordon Enderle

Actuarial work involves modeling future contingent events that are uncertain in terms of timing, frequency and severity. Understanding the central tendency of a contingency and its possible distribution is critical for an actuary to help individuals and institutions manage risk. This course starts with a brief discussion of data analysis, focusing on the central tendency and distribution of data. Introductory probability concepts are introduced next. The course concludes with a study of discrete probability models with an eye toward actuarial application.

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What's inside

Learning objectives

Those enrolled in probability for actuaries: introduction to discrete distribution will learn to:
Describe basic data types
Describe the central tendency measures of datasets: mean, median and mode
Describe the dispersion measures of datasets: range, percentiles and variance
Describe basic probability concepts including sample space, events and set operations
Calculate probabilities for simple discrete events
Differentiate between a discrete and continuous random variable

Describe bayes theorem, conditional probability, law of total probability and statistical independence
Describe and use a probability mass function, probability density function and cumulative distribution function
Describe and calculate the mathematical expectation of a random variable
Describe the features and application of the following discrete distributions: uniform, binomial, poisson
Calculate probabilities for random variables governed by a uniform, binomial or poisson distribution
Describe the features and application of the following discrete distributions: geometric, negative binomial
Calculate probabilities for random variables governed by a geometric or negative binomial distribution

Those enrolled in probability for actuaries: introduction to discrete distribution will learn to:
Describe basic data types
Describe the central tendency measures of datasets: mean, median and mode
Describe the dispersion measures of datasets: range, percentiles and variance
Describe basic probability concepts including sample space, events and set operations
Calculate probabilities for simple discrete events
Differentiate between a discrete and continuous random variable
Describe bayes theorem, conditional probability, law of total probability and statistical independence
Describe and use a probability mass function, probability density function and cumulative distribution function
Describe and calculate the mathematical expectation of a random variable
Describe the features and application of the following discrete distributions: uniform, binomial, poisson
Calculate probabilities for random variables governed by a uniform, binomial or poisson distribution
Describe the features and application of the following discrete distributions: geometric, negative binomial
Calculate probabilities for random variables governed by a geometric or negative binomial distribution

Good to know

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Covers math and statistical theory that's commonly found in actuarial work

Offers a mix of text-based lessons, videos, and interactive exercises

Provides a strong grasp of the foundational concepts of probability theory

Taught by seasoned instructors who have made significant contributions to the field of actuarial science

Employs a variety of real-world examples to illustrate the practical applications of probability theory in actuarial work

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Activities

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Career center

Learners who complete Probability for Actuaries: Introduction to Discrete Distribution will develop knowledge and skills that may be useful to these careers:

Actuary

Actuaries are responsible for assessing and managing financial risk. They use mathematical and statistical techniques to analyze data and develop models that can predict future events. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for actuaries. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for actuaries who want to be able to accurately assess and manage risk.

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Insurance Underwriter

Insurance underwriters assess and manage risk for insurance companies. They use mathematical and statistical techniques to analyze data and develop models that can predict the likelihood of an event occurring. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for insurance underwriters. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for insurance underwriters who want to be able to accurately assess and manage risk.

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Financial Analyst

Financial analysts provide investment advice to individuals and institutions. They use mathematical and statistical techniques to analyze data and develop models that can predict the performance of financial investments. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for financial analysts. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for financial analysts who want to be able to accurately assess and manage risk.

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Data Analyst

Data analysts use mathematical and statistical techniques to analyze data and develop models that can be used to make decisions. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for data analysts. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for data analysts who want to be able to accurately analyze data and develop models.

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Risk Manager

Risk managers assess and manage risk for organizations. They use mathematical and statistical techniques to analyze data and develop models that can predict the likelihood of an event occurring. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for risk managers. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for risk managers who want to be able to accurately assess and manage risk.

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Business Analyst

Business analysts use mathematical and statistical techniques to analyze data and develop models that can be used to make decisions. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for business analysts. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for business analysts who want to be able to accurately analyze data and develop models.

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Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for statisticians. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for statisticians who want to be able to accurately collect, analyze, and interpret data.

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Quantitative Analyst

Quantitative analysts use mathematical and statistical techniques to analyze data and develop models that can be used to make decisions. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for quantitative analysts. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for quantitative analysts who want to be able to accurately analyze data and develop models.

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Mathematician

Mathematicians use mathematical and statistical techniques to solve problems. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for mathematicians. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for mathematicians who want to be able to accurately solve problems.

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Computer Scientist

Computer scientists use mathematical and statistical techniques to design and develop computer systems. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for computer scientists. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for computer scientists who want to be able to accurately design and develop computer systems.

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Software Engineer

Software engineers use mathematical and statistical techniques to design and develop software. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for software engineers. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for software engineers who want to be able to accurately design and develop software.

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Operations Research Analyst

Operations research analysts use mathematical and statistical techniques to solve problems related to the design and operation of systems. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for operations research analysts. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for operations research analysts who want to be able to accurately solve problems related to the design and operation of systems.

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Financial Risk Manager

Financial risk managers use mathematical and statistical techniques to assess and manage financial risk. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for financial risk managers. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for financial risk managers who want to be able to accurately assess and manage financial risk.

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Data Scientist

Data scientists use mathematical and statistical techniques to collect, analyze, and interpret data. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for data scientists. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for data scientists who want to be able to accurately collect, analyze, and interpret data.

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Investment Analyst

Investment analysts use mathematical and statistical techniques to analyze data and develop models that can be used to make investment decisions. Probability for Actuaries: Introduction to Discrete Distribution provides a solid foundation in probability theory, which is essential for investment analysts. The course covers topics such as probability distributions, Bayes' theorem, and the law of total probability. This knowledge is essential for investment analysts who want to be able to accurately analyze data and develop models.

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Reading list

We've selected 23 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Probability for Actuaries: Introduction to Discrete Distribution.

An Introduction to Probability and Statistics

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This textbook provides a solid foundation in probability and statistics. It covers a wide range of topics, including probability distributions, statistical inference, and regression analysis. The book also includes numerous examples and exercises to help students understand the material.

An Introduction to Probability and Statistics...

Hardcover

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