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Q1. Find the probability of getting (i) exactly 4 heads and (ii) not more than 4 heads when 6 coins are tossed. 10 Q2. Determine the probability distribution for the number of white beads among 5 beads drawn at random from a bowl containing 4 white and 7 black beads. Using this to compute the mean and variance and check the results by using the formulae. 10 Q3. If for the binomial distribution, b(x; n, p). n = 4 and, also P(X = 2) = 3P(X = 3). What is the value of p? 10 Q4. Let X be a random variable with probability distribution. X 1 2 4 5 f(x) 0.2 0.3 0.2 0.2 0.1 Find the probability function of 3X-1, X2, and X2 + 2 and find E(3X - 1),E(X?) and E(X2 + 2). 10 Q5. An insurance salesman sells policies to 5 men, all of identical age and in good health. According to the actuarial tables, the probability that a man of this particular age will be alive 30 years hence is 2/3. Find the probability that in 30 years (i) All men (ii) At least 3 men (iii) Only two men (iv) At most one man will be alive. 10