Let X1, X2, X3, "" be a sequence of independent samples of a random variable X with mean u and variance o. We define a new random sequence Y1, Y2, Y3, .". as Y1 = X1 - X2 and Yn = Xzn-1 - Xzn- (a) Find the mean and variance of the sample average Y = = EN_, Y,. (b) If the independent and identically distributed sequence X1, X2, X3, ... has u = 75 and standard deviation o = 15, determine how many samples / is needed to guarantee that the sample mean X = = _N_, XD is between 74 and 76 with probability 0.99