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., R_{X}
= {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*.

Tags : Introduction , 12th Business Maths and Statistics : Chapter 6 : Random Variable and Mathematical Expectation

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

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