1. (a) For each one of the statements below say whether the statement is true or false, explaining your answer. i. Let A and B be two events such that P( A) > 0 and P(B) > 0. If it holds that P(A | B) = 0, then P(B| A) - 1 ii. For two independent events A and B such that P(A) > 0 and P(B) > 0, then: P(AUB) = P(A) + P(B). iii. For a random variable X, then: Var(X) > Var(X + 2). iv. A random sample of size n is a sequence of n independent and non-identically distributed random variables. v. The standard normal distribution has fatter tails than the Student's t distribution with finite degrees of freedom