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(X+Y)=E(X)+E(Y).
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Expert Answer

lamusesamuset
Answered 2021-02-10 Author has 93 answers
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.
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