Conditional Expected Value Calculator

Formula

To calculate the Conditional Expected Value:

\[ E(X|C) = X \times P(X|C) \]

Where:

\(E(X|C)\) is the Conditional Expected Value
\(X\) is the value of the random variable
\(P(X|C)\) is the probability of \(X\) given the condition \(C\)

What is Conditional Expected Value?

Conditional Expected Value is a statistical measure that calculates the expected value of a random variable given that a certain condition is met. It is a refinement of the concept of expected value, which takes into account additional information or constraints.

This measure is particularly useful in scenarios where the outcome of interest is influenced by certain conditions or events. For example, in finance, the conditional expected value might be used to estimate the expected return on an investment given certain market conditions. In general, it helps in making more informed decisions by considering the impact of specific conditions on the expected outcome.

Example Calculation 1

Let's assume the following values:

Value of the Random Variable (X) = 10
Probability of X given the Condition (P(X|C)) = 0.5

Using the formula:

\[ E(X|C) = 10 \times 0.5 = 5 \]

The Conditional Expected Value is 5.

Example Calculation 2

Let's assume the following values:

Value of the Random Variable (X) = 20
Probability of X given the Condition (P(X|C)) = 0.3

Using the formula:

\[ E(X|C) = 20 \times 0.3 = 6 \]

The Conditional Expected Value is 6.