Probability Trees and Conditional Expectations

The expected value of a random variable is the probability-weighted average of the possible outcomes of the random variable.

For a random variable X, the expected value of X is denoted E(X).

where $X_i$ is one of n possible outcomes of the discrete random variable X.

The variance of a random variable is the expected value (the probability-weighted average) of squared deviations from the random variable’s expected value:

The two notations for variance are $\sigma^2(X)$ and Var(X).

where $X_i$ is one of n possible outcomes of the discrete random variable X.