Introduction to Probability Theory (saylor.org)

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This course will introduce you to the fundamentals of probability theory and random processes. The theory of probability was originally developed in the 17th century by two great French mathematicians, Blaise Pascal and Pierre de Fermat, to understand gambling.

Today, the theory of probability has found many applications in science and engineering. Engineers use data from manufacturing processes to sample characteristics of product quality in order to improve the products being produced. Pharmaceutical companies perform experiments to determine the effect of a drug on humans and use the results to make decisions about treatment of illnesses, while economists observe the state of the economy over periods of time and use the information to forecast the economic future.

In this course, you will learn the basic terminology and concepts of probability theory, including random experiments, sample spaces, discrete distribution, probability density function, expected values, and conditional probability. You will also learn about the fundamental properties of several special distributions, including binomial, geometric, normal, exponential, and Poisson distributions, as well as how to use them to model real-life situations and solve applied problems.

Upon successful completion of this course, you will be able to:

- define probability,sample space, events, and probability functions;

- use combinations to evaluate the probability of outcomes in coin-flipping experiments;

- calculate the probability of union and intersection of events and conditional probability;

- apply Bayes’ theorem to simple situations;

- calculate the expected values of discrete and continuous random variables;

- determine the distribution of the sums of random variables;

- calculate cumulative distributions and marginal distributions;

- use random processes to model and predict phenomena governed by binomial, multinomial, geometric, exponential, normal, and Poisson distributions; and

- explain and use the law of large numbers and the central limit theorem.

Course Requirements:have completed Single-Variable Calculus I, Single-Variable Calculus II, Multivariable Calculus , Linear Algebra and Differential Equations, or their equivalents.

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