Expected Value of a sequence with two random variables

1. How do you find the expected value of two random variables?
2. How do you find the expected value of a sequence?
3. How do you find the expected value of multiple events?
4. What happens to the variance when you add 2 random variables?

How do you find the expected value of two random variables?

For any two random variables X and Y , E(X+Y)=E(X)+E(Y) E ( X + Y ) = E ( X ) + E ( Y ) That is, the expected value of the sum is the sum of expected values, regardless of how the random variables are related.

How do you find the expected value of a sequence?

The mean or expected value of X is defined by E(X) = sum xk p(xk).

How do you find the expected value of multiple events?

In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.

What happens to the variance when you add 2 random variables?

Theorem: The variance of the sum of two random variables equals the sum of the variances of those random variables, plus two times their covariance: Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y).