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

If X and Y are random variables and c is any constant, show that $E\left(X-Y\right)=E\left(X\right)-E\left(Y\right)$.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

faldduE
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, E(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.