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# Random variable

A random variable is a variable that is subject to randomness, which means it could take on different values.

Random variable

Introduction:

Let the random experiment be the toss of a coin. When ‘n’ coins are tossed, one may be interested in knowing the number of heads obtained. When a pair of dice is thrown, one may seek information about the sum of sample points. Thus, we associate a real number with each outcome of an experiment. In other words, we are considering a function whose domain is the set of possible outcomes and whose range is subset of the set of real numbers. Such a function is called random variable.

In algebra, you learned about different variables like X or Y or any other letter in a particular problem. Thus in basic mathematics, a variable is an alphabetical character that represents an unknown number. A random variable is a variable that is subject to randomness, which means it could take on different values. In statistics, it is quite general to use X to denote a random variable and it takes on different values depending on the situation.

Some of the examples of random variable:

(i) Number of heads, if a coin is tossed 8 times.

(ii) The return on an investment in one-year period.

(iii) Faces on rolling a die.

(iv) Number of customers who arrive at a bank in the regular interval of one hour between 9.00 a.m and 4.30 p.m  from Monday to Friday.

(v)  The sale volume of a store on a particular day.

For instance, the random experiment ‘E’ consists of three tosses of a coin and the outcomes of this experiment forms the sample space is ‘S’. Let X denotes the number of heads obtained. Here X is a real number connected with the outcome of a random experiment E. The details given below Outcome (ω)         : (HHH) (HHT) (HTH) (THH) (HTT) (THT) (TTH) (TTT)

Values of X = x :   3      2        2        2        1        1        1        0

i.e., RX  = {0, 1, 2, 3}

From the above said example, for each outcomes ω, there corresponds a real number X(ω)Since the points of the sample space ‘S’ corresponds to outcomes is defined for each ω S.

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12th Business Maths and Statistics : Chapter 6 : Random Variable and Mathematical Expectation : Random variable | Introduction