Notes On Random Variable - CBSE Class 12 Maths
A random experiment is an experiment that has more than one possible result, and it is not possible to predict the result in advance. The result of each trial in a random experiment is called an outcome, and the collection of all such possible outcomes is called the sample space. In tossing two coins, we may want the number of heads that appear. In rolling two dice, we may want the sum of the numbers on the two dice. In an experiment of drawing 3 balls at random from an urn containing 6 blue and 7 red balls, we may want to know the number of blue balls in the sample of 3 balls. In tossing two coins, the number of heads that appear in an outcome could be 2, 1 or 0. In rolling two dice, the sum of the numbers in each outcome could be 2, 3, 4 … or 12. In the balls experiment, the number of blue balls could be 0, 1, 2 or 3. The value of the variable depends on the random experiment, and hence, it is called a random variable. It is denoted by X. Tossing two coins: Sample space (S): {HH, HT, TH, TT} Rule: Number of heads that appear. Let X denote the number of heads that appear. Number of heads in (HH) = X(HH) = 2 X(HT) = 1 X(TH) = 1 X(TT) = 0 Let Y denote the number of tails that appear. Number of tails in HH = Y(HH) = 0 Y(HT) = 1 Y(TH) = 1 Y(TT) = 2 Domain = {HH, HT, TH, TT} Co-domain = {0, 1, 2} A random variable is a real valued function whose domain is the sample space of a random experiment.

#### Summary

A random experiment is an experiment that has more than one possible result, and it is not possible to predict the result in advance. The result of each trial in a random experiment is called an outcome, and the collection of all such possible outcomes is called the sample space. In tossing two coins, we may want the number of heads that appear. In rolling two dice, we may want the sum of the numbers on the two dice. In an experiment of drawing 3 balls at random from an urn containing 6 blue and 7 red balls, we may want to know the number of blue balls in the sample of 3 balls. In tossing two coins, the number of heads that appear in an outcome could be 2, 1 or 0. In rolling two dice, the sum of the numbers in each outcome could be 2, 3, 4 … or 12. In the balls experiment, the number of blue balls could be 0, 1, 2 or 3. The value of the variable depends on the random experiment, and hence, it is called a random variable. It is denoted by X. Tossing two coins: Sample space (S): {HH, HT, TH, TT} Rule: Number of heads that appear. Let X denote the number of heads that appear. Number of heads in (HH) = X(HH) = 2 X(HT) = 1 X(TH) = 1 X(TT) = 0 Let Y denote the number of tails that appear. Number of tails in HH = Y(HH) = 0 Y(HT) = 1 Y(TH) = 1 Y(TT) = 2 Domain = {HH, HT, TH, TT} Co-domain = {0, 1, 2} A random variable is a real valued function whose domain is the sample space of a random experiment.

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