In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated Examples · History · Definitions · L random variables

Learn how the conditional expected value of a random variable is defined. Discover how it is calulated through examples and solved exercises.

The measure-theoretic definition of conditional expectation is a bit unintuitive, but we will show how it matches what we already know from earlier study.

Conditional expectations such as E[X|Y = 2] or E[X|Y = 5] are numbers. If we consider E[X|Y = y], it is a number that depends on y. So it is a function of y.

This section reviews conditional distribution functions and expectation as usually presented in more elementary probability and statistics courses, under the ...

20 апр. 2022 г. · We interpret the conditional probability of A given B as the probability that. A occurs, given the additional information that B occurs.

One of the most useful concepts in probability theory is that of conditional prob- ability and conditional expectation. The reason is twofold.

Definition: Let X and Y be discrete random variables. The conditional probability function of X, given that Y = y, is: P(X = x|Y = y) = P(X = x AND Y = y) P(Y ...

In fact, conditional expectation is the expectation on a new probability space, for an observer for whom the probabilistic hypothesis is affected by his/her ...

Conditional Expectation as a Function of a Random Variable: Remember that the conditional expectation of X given that Y=y is given by E[X|Y=y]=∑xi∈RXxiPX|Y( ...