Solutions of chapter 32. Mean and Variance of a Random Variable | RD Sharma - Mathematics (Volume 2)

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Which of the following distributions of probabilities of a random variable X are the probability distributions?

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Which of the following distributions of probabilities of a random variable X are the probability distributions?

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Which of the following distributions of probabilities of a random variable X are the probability distributions?

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Which of the following distributions of probabilities of a random variable X are the probability distributions?

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A random variable X has the following probability distribution:

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A random variable X has the following probability distribution:

Determine:

i. The value of a

ii. P (X<3), P (X≥3), P(0<X<5).

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The probability distribution function of a random variable X is given by

where c > 0

Find:

i. c ii. P(X<2)

iii. P(1<X≤2)

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Let X be a random variable which assumes values x₁, x₂, x₃, x₄ such that 2P(X = x₁) = 3P (X = x₂) = P (X = x₃) = 5P(X = x₄). Find the probability distribution of X.

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A random variable X takes the values 0, 1, 2 and 3 such that:

P(X = 0) = P(X>0) = P(X<0);

P(X = -3) = P(X = -2) = P(X = -1);

P (X = 1) = P(X = 2) = P(X = 3).

Obtain the probability distribution of X.

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Two cards are drawn from a well-shuffled pack of 52 cards. Find the probability distribution of the number of aces.

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Find the probability distribution of the number of heads, when three coins are tossed.

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Four cards are drawn simultaneously from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number of aces.

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A bag contains 4 red and 6 black balls. Three balls are drawn at random. Find the probability distribution of the number of red balls.

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Five defective mangoes are accidentally mixed with 15 goods ones. Four mangoes are drawn at random from this lot. Find the probability distribution of the number of defective mangoes.

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Two dice are thrown together, and the number appearing on them noted. X denotes the sum of the two numbers. Assuming that all the 36 outcomes are equally likely, what is the probability distribution of X?

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A class has 15 students whose ages are 14, 17, 15, 14, 21, 19, 20, 16, 18, 17, 20, 17, 16, 19 and 20 years respectively. One student is selected in such a manner that each has the same chance of being selected and the age X of the selected student is recorded. What is the probability distribution of the random variable X?

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Five defective bolts are accidentally mixed twenty good ones. If four bolts are drawn at random from this lot, find the probability distribution of the number of defective bolts.

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Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.

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Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Find the probability distribution of the number of kings.

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Two cards are drawn successively without replacement from a well-shuffled pack of 52 cards. Find the probability distribution of the number of aces.

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Find the probability distribution of the number of white balls drawn in a random draw of 3 balls without replacement, from a bag containing 4 white and 6 red balls.

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Find the probability distribution of Y in two throws of two dice, where Y represents the number of times a total of 9 appears.

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From a lot containing 25 items, 5 of which are defective, 4 are chosen at random. Let X be the number of defectives found. Obtain the probability distribution of X if the items are chosen without replacement.

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Three cards are drawn successively with replacement from a well-shuffled deck of 52 cards. A random variable x denotes the number of hearts in the three cards drawn. Determine the probability distribution of X.

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An urn contains 4 red and 3 blue balls. Find the probability distribution of the number of blue balls in a random draw of 3 balls with replacement.

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Two cards are drawn simultaneously from a well-shuffled deck of 52 cards. Find the probability distribution of the number of successes, when getting a spade is considered a success.

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A fair die is tossed twice. If the number appearing on the top is less than 3, it is a success. Find the probability distribution of number of successes.

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An urn contains 5 red and 2 black balls. Two balls are randomly selected. Let X represent the number of black balls. What are the possible values of X? Is X a random variable?

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Let X represent the difference between the number of heads and the number of tails when a coin is tossed 6 times. What are the possible values of X?

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From a lot of 10 bulbs, which includes 3 detectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.

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Four balls are to drawn without replacement from a box containing 8 red and 4 white balls. If X denotes the number of red balls drawn, find the probability distribution of X.

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The probability distribution of a random variable X is given below:

i. Determine the value of k

ii. Determine P (X≤2) and P(X>2)

iii. Find P (X≤2) + P (X>2)

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Let X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that

Where k is a positive constant.

Find the value of k. Also, find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.

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