Problem understanding the Expectation Operator

1. What does the expectation operator do?
2. How do you find the expectation of a function?
3. How do you find the expected value of XY?

What does the expectation operator do?

The expectation operator takes a random variable and gives you its average value, the variance operator takes a random variable and gives you its variance. You should get used to using the expectation and variance operators.

How do you find the expectation of a function?

To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E ( X ) = μ = ∑ x P ( x ) .

How do you find the expected value of XY?

To obtain E(XY), in each cell of the joint probability distribution table, we multiply each joint probability by its corresponding X and Y values: E(XY) = x₁y₁p(x₁,y₁) + x₁y₂p(x₁,y₂) + x₂y₁p(x₂,y₁) + x₂y₂p(x₂,y₂).