Partial Differential Equations

This section explores the concept of expectation (mean) in random variables, its computation for both discrete and continuous cases, and its applications in solving real-world engineering problems.

What Is Expectation (Mean)?

Expectation (mean) is the long-run average value of a random variable's outcomes, serving as a foundational concept in probability and statistics.

Expectation For Discrete Random Variables

This section discusses the concept of expectation (mean) for discrete random variables, detailing its definition and calculation methods.

Expectation For Continuous Random Variables

This section covers the expectation (mean) of continuous random variables, its definition, computation formula, properties, and applications in real-world scenarios.

Properties Of Expectation

This section explores the fundamental properties of expectation, including linearity, the expectation of constants, and the multiplicative property for independent variables.

Variance And Relation To Expectation

This section addresses the concept of variance in relation to the expectation of random variables, emphasizing its role in measuring spread around the mean.

Expectation In Applications Of Pdes

This section discusses the concept of expectation within the context of Partial Differential Equations (PDEs), emphasizing its role in stochastic models and applications such as finance and heat equations.

Summary

Expectation, or mean, measures the average outcome of a random variable, crucial in probability, statistics, and applied mathematics.

Practice Problems

This section provides practical problems to solidify understanding of the expectation (mean) of random variables.