Given:

n random variables \(X_{1},X_{2},....,X_{n}\)

Formula used:

\(E(X_{1},+ X_{2},...,+ X_{n})=E(X_{1})+E(X_{2})+...+E(X_{n})\)

Linearity means additivity over the variables. Thus (1) expresses the fact that expectation is additive over the random variables, in other words, expectation is a linear function.

n random variables \(X_{1},X_{2},....,X_{n}\)

Formula used:

\(E(X_{1},+ X_{2},...,+ X_{n})=E(X_{1})+E(X_{2})+...+E(X_{n})\)

Linearity means additivity over the variables. Thus (1) expresses the fact that expectation is additive over the random variables, in other words, expectation is a linear function.