During engineering design, instead of working with exact probability expressions, it is sometimes easier to use a clean upper bound on the probability expressions for system optimizations. In this problem, you will be using the Chernoff bound to determine some useful probability upper bounds. (a) Use the Chernoff bound to prove that Q(x) x) where X is a normal distribution. (b) Let Y = EX; where the X; are i.i.d. Bernoulli random variables with param- eter p. Using the Chernoff bound, prove that e P(Y 2 (1 + 6)np) (1+6)1+6) 0