Question

Prove that E(cX)=cE(X), where c is a constant.

Answer 1

By definition:
E(x)
= ( ∑ xi )/ n

this means that
E(cx)
= ( ∑ cxi )/ n
= ( c ∑ xi )/ n    [ by taking out the common factor c]
= c ( ∑ xi )/ n
= c E(x)

Conclusion: proved  E(cx)=cE(x)