# If X and Y are random variables and c is any constant, show that E(X+Y)=E(X)+E(Y).

Random variables
If X and Y are random variables and c is any constant, show that $$E(X+Y)=E(X)+E(Y)$$.

2021-02-10
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.