4-36. Verify that if X is a discrete or continuous random variable whose expectation exists, then, for a and b constants:

(a) E

(a) = a

(b) E(a ± bX) = a ± bE(X)

For finite k, demonstrate that:

(c) E 5kj

=1 gj(X)6 = kj

=1 E(gj(X)), where gj(X) is a function of the random variable X.