Random World and Random Variables

We live in a random world; hence it is a multidimensional probability space. In our world some part are deterministic, these can be controlled by us and probability has no role in it. But our “random world” is governed by multiple random variables. This fact is illustrated by the following example of use of a mobile phone.

One dimensional random variables

Number of phone calls made per day by a person: Discrete Random Variable

Number of wrong numbers made by a person per day: Discrete Random Variable

Time spent on a phone call by a person: Continuous Random Variable

Time between two phone calls made by a person in a day: Continuous Random Variables

Two dimensional random variables

Marks obtained by an undergraduate student in two internal assessments: Discrete Random Variables

Weight and height of a second year undergraduate student: Continuous Random Variables

Multidimensional (n) random variables

Time spent on each of n phone calls made per day by an individual: n dimensional continuous random variable

No. of phone calls made per day by n members of a family: n dimensional discrete random variable

Here n is also a one dimensional random variable