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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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.

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,

Here, F(X) is the expected value of X and E(Y) is the expected value of Y.

Therefore, the relation

Conclusion:

Hence, the relation

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