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Question 3 (10 marks) Let A, B. C be three events with P(A) > 0, P(B) > 0 and P(C) >:0. For each of the following statements, determine whether it is true or false. If it is true, give a proof; if it is false, give a counterexample. (a) If P(AUB) = P(A) + P(B), then An B = 0. ages after page 28 - Page 5 of 28 (b) If P(A BnC) = P(A|B), then P(AnC B) = P(AIB)P(C B).(c) Assume that A, B and C satisfy two assumptions: (i) A and B are mutually independent, (ii) A and C are mutually independent; then A and BOC are mutually independent.(d) If f and g are two probability density functions, then }(f + 9) is also a probability density function. pages after page 28 - Page 6 of 28 (e) For a continuous nonnegative random variable X, if E(X") exists, then E(X ) exists