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

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

2021-01-06
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, E(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.

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