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3. (a) A fair dice is tossed 6 times. Suppose A is the event that the number of occurrences of an even digit equals the number of occurrences of an odd digit, while B is the event that at most three odd digits will occur i. Determine with reason if the events A and B are mutually exclusive. ii. Determine the probabilities of the events A and B. Are the events A and B independent? b) Suppose a fair coin is tossed 8 times. Let X be the discrete random variable representing the number of heads which can occur i. Determine the discrete probability distribution of X i. Determine the Expected value ? = E(X) of X iii. Determine the Variance, Var(x), of X iv. Determine the Standard Deviation. ?, of X

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