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Addition and multiplication formulas for expected value & variance

Expected Value in statistics is the product of multiplying each outcome with the possibility of occurrence of those outcomes and then adding up the values.

To figure out the Variance, one has to calculate the average of the set of numbers and then subtract this average from each number and square the differences. The average of these squared differences gives out the variance.

**Addition and Multiplication formulae for Expected Value & Variance are as follows:**

Let us consider X and Y to be random variables, then the formulas would be:

E(X+Y) = E(X) + E(Y)

E(aX) = a.E(X)

Var(X) = E(x^2) – E(〖x)〗^2

Var(aX) = a^2.var(X)

Var(X+a) = var(X)

These equations stand when a € R. When X and Y are independent, there are two more equations:

E(X.Y) = E(X) . E(Y)

Var (X+Y) = Var(X) + Var(Y).

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