Proof of THM 2: Variance . Definition: the variance of a R. V. X is defined as Var (X): = E[(X - EX)2]. . Remarks: 1. Var(X) is always positive 2. Alternatively, Var(X) = E(X2] - E[X]2Concentration bound . E[[X - EXI] 1, we always have Pr[[X - EX| 2 Co] S ~z for o = Var(X) 26 30Problem 1 (30 points). Prove the following claims and show your calculations. (a) Prove that E[Y]