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Mathematics : Probability

Short Answer Type

971. Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as:
six appears on at least one die

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972. Find the mean μ, variance σ² for the following probability distribution:

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973. Find the mean μ, variance σ² for the following probability distribution:

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Long Answer Type

974. Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

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975. Find the mean number of heads in three tosses of a fair coin.

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976. Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

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977. Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.

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978. Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings.

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979. Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

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980. A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19, 20 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 X ? Find mean, variance and standard deviation of X.

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