Let X~ N(0, 2) be a zero mean Gaussian random variable. (a) Let X1, X2,... be IID random variables with the same distribution as X. Let Sn = X+X+...+Xn For > 0, establish the Chernoff bound on P(|Sn ne). (b) Let Z be a random variable such that Z = 1 with probability 1/2 and Z = -1 with probability 1/2. Show that Z is a sub-Gaussian random variable and find its parameter. (c) Let Z, Z2,... be IID random variables. Using the sub-Gaussian property or otherwise, find the Chernoff bound on