Q. 17. Suppose that two cards are drawn at random from a deck of cards. Let be the number of aces obtained. Then the value of is Choose the correct answer in the following:
Q. 16 The mean of the numbers obtained on throwing a die having written 1 on three faces, on two faces and on one face is, Choose the correct answer in the following:
Q. 15. In a meeting, of the members favour and oppose a certain proposal. A member is selected at random and we take . if he opposed, and if he is in favour. Find and Var .
Q. 14 A class has students whose ages are and years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable Find mean, variance and standard deviation of .
Q. 13 Let denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of.
Q. 12 Two numbers are selected at random (without replacement) from the first six positive integers. Let denote the larger of the two numbers obtained. Find
Q. 9 The random variable has a probability distribution of the following form, where k is some number :
Q. 9. The random variable X has a probability distribution P(X) of the following form, where k is some number :
(a) Determine the value of
Q. 7 A coin is biased so that the head is times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.
Q. 6. From a lot of bulbs which include defectives, a sample of bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
Q . 5 Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as
(ii) six appears on at least one die.
Q. 5 Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as
(i) number greater than 4
Q. 4 Find the probability distribution of
(ii) number of tails in the simultaneous tosses of three coins.