 # If X and Y are random variables and c is any constant, show that E(X+Y)=E(X)+E(Y). Wierzycaz 2021-02-09 Answered
If X and Y are random variables and c is any constant, show that $E\left(X+Y\right)=E\left(X\right)+E\left(Y\right)$.
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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,
$E\left(X+Y\right)=E\left(X\right)+E\left(Y\right)$
Here, F(X) is the expected value of X and E(Y) is the expected value of Y.
Therefore, the relation $E\left(X+Y\right)=E\left(X\right)+E\left(Y\right)$ is proved if X and Y are random variables and c is any constant.
Conclusion:
Hence, the relation $E\left(X+Y\right)=E\left(X\right)+E\left(Y\right)$ is proved if X and Y are random variables and c is any constant.