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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Answer 1

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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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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