For a random variable X, prove (a) (d) of Theorem 2 6 2 (a) E(c) c (b) E cg(X) cE g(X) (c) E igi(X) iE gi(X) (d) Var(aX b) a2 Var(X) In particular, Var(aX) a2 Var(X)

Question: For a random variable X, prove (a)-(d) of Theorem 2.6.2. (a) E(c) = c. (b) E[cg(X)] = cE [g(X)]. (c) E[igi(X)] = iE[gi(X)]. (d) Var(aX

For a random variable X, prove (a)-(d) of Theorem 2.6.2.
(a) E(c) = c.
(b) E[cg(X)] = cE [g(X)].
(c) E[Σigi(X)] = ΣiE[gi(X)].
(d) Var(aX + b) = a2 Var(X). In particular, Var(aX) =a2 Var(X).

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