Answer TURE or FALSE for these six questions and explain reason simply.

1. Let A, B be events defined in a common probability space. Suppose that P(A) 1. Then, Var (X) > Var (Y). 3. Let {Xx}, k = 1, 2, . .. be a random sequence with Cov(Xi, Xj) and Cor(Xi, X;) denoting the autocovariance and autocorrelation respectively. Then, Cov(Xi, Xj) 0.1. 5. Let {X(t) } be a random process with X(t) = e At where A is a random variable uniformly distributed over [-1, 1]. Then, {X(t) } is weakly stationary. 6. Let Sn = - EL aiXi where all Xi are independent identically distributed (iid) random variables with E[Xi] = 0 and Var[Xi] = 1 for all 2 = 1, ...,n and ai are given positive real numbers with ai # aj for i # j. Then, by the Strong Law of Large Numbers the sequence {Sn}, n = 1, 2, ... converges to 0 with probability 1