Random variables are generally classified into two types, based on the values they take such as Discrete random variable and Continuous random variable.

**Discrete
and Continuous random variables**

Random variables are generally classified into two types, based
on the values they take such as Discrete random variable and Continuous random
variable.

A random variable is said to be discrete if it takes only a
finite or countable infinite number of values.

Consider the experiment of tossing a coin

If *X* (Head) =1, *X* (Tail) = 0

Then *X* takes the
values either 0 or 1

This is a discrete random variable.

Consider the experiment of tossing a coin till head appears.

Let random variable *X*
denote the number of trials needed to get a head. The values taken by it will
be 1, 2, 3, ..

It is discrete random variable taking countable infinite values.

A random variable *X* is
said to be continuous, if it takes values in an interval or union of disjoint
intervals. (A rigorous definition is beyond the scope of the book).

If *X* is defined as the
height of students in a school ranging between 120 cms and 180 cms, Then the
random variable *X* is {*x*/120 *cms* < *x* < 180 cms }
is a continuous random variable.

Let the maximum life of electric bulbs is 1500 hrs. Life time of
the electric bulb is the continuous random variables and it is written as *X* = {*x*/0
≤ *x* ≤ 1500}

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11th Statistics : Chapter 9 : Random Variables and Mathematical Expectation : Discrete and Continuous random variables |

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