Given two events A and B , state whether each of the following can be possible or not  a) P(A) P(A) c) P(A n B) = 0.12 and P(A u B ) = 0.20 d) P(A n B) = P(A)P(B) and P(B) > P(B \ A) e) P(A) + P(B) = 1.2

(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. 4 i. 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. istribution with

Event E and event F are independent. Fiven P(E) = 0.3, P = (F) 0.5, compute P(E and F) and P(E or F). a) P(E and F) = b ) P(E or F)

2b) Find zo for the following probabilities: i) P(Z > Zo) - 0.25 O-0.67 O o 0.67 O 0.5 Jimmy and Rosalynn Carter celebrate 76 years of marm to