981.In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).
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Long Answer Type
982.Find the variance of the number obtained on a throw of an unbiased die.
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983.A die is tossed twice. Getting a number greater than 4 is considered a success. Find the variance of the probability distribution of the number of successes.
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984.Two bad eggs are mixed accidentally with 10 good ones. Three eggs are drawn at random without replacement from this lot. Find the mean and variance for the number of bad eggs.
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985.Three bad eggs got mixed up with 7 good eggs. If three eggs are drawn (without replacement) from 10 eggs, find the mean and variance for the number of bad eggs among them.
986.Five defective bulbs are accidentally mixed with twenty good ones. It is not possible to just look at a bulb and tell whether or not a bulb is defective. Four bulbs are drawn at random from this lot. Find the mean number of defective bulbs drawn.
Let us denote by X, the number of defective bulbs. Clearly X can take the values 0, 1, 2, 3, 4. P(X = 0) = (no defective bulb) = P(all 4 Â goods ones) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â P(X = 1) = P(1 defective and 3 good ones)
       Â
P(X = 2) = P(2 defective and 2 Â good ones)
       Â
P(X  = 3) = P(3 defective and one good one)         P(X = 4) = P(all 4 defective)             ∴ Probability distribution table is
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987.Two cards are drawn simultaneously (or successively, without replacement) from a well-shuffled deck of 52 cards. Compute σ2 for the number of aces.
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988.In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.
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Multiple Choice Questions
989.The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is
1
2
5
5
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990.Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is
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