Given:

The two random variables are X and Y.

The constant number is C.

Approach:

As it is possible to take expectations through any linear combination of random variables.

Therefore,

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

Here, F(X) is the expected value of X and E(Y) is the expected value of Y.

Therefore, the relation \(E(X + Y) = E(X) + E(Y)\) is proved if X and Y are random variables and c is any constant.

Conclusion:

Hence, the relation \(E (X + Y) = E(X) + E(Y)\) is proved if X and Y are random variables and c is any constant.

The two random variables are X and Y.

The constant number is C.

Approach:

As it is possible to take expectations through any linear combination of random variables.

Therefore,

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

Here, F(X) is the expected value of X and E(Y) is the expected value of Y.

Therefore, the relation \(E(X + Y) = E(X) + E(Y)\) is proved if X and Y are random variables and c is any constant.

Conclusion:

Hence, the relation \(E (X + Y) = E(X) + E(Y)\) is proved if X and Y are random variables and c is any constant.