The formula to calculate the Conditional Variance is:
\[ Var(Y | X) = E(Y^2 | X) - [E(Y | X)]^2 \]
Where:
Conditional variance is a measure of the variability of a random variable Y given that another random variable X is known. It provides insight into how the distribution of Y changes when X is fixed. This concept is particularly useful in statistics and probability theory, where it helps in understanding the relationship between two random variables. Conditional variance is used in various fields such as finance, economics, and engineering to model and predict outcomes based on known conditions.
Let's assume the following values:
Using the formula to calculate the Conditional Variance:
\[ Var(Y | X) = 25 - 4^2 = 25 - 16 = 9 \]
The Conditional Variance (Var(Y | X)) is 9.
