Question

Define Random Variable. Explain different variables and their importance in the study of statistics.

Answer 1

Random Variable is a set of all possible values from the outcomes of a random experiment.

For example If we toss a coin ,It would have two outcomes

1) Heads

2) Tails

so the random variable can take up the value of heads or tails.

The  two types of random variables are

1) Discrete random variables

A discrete random variable can take only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the total number of members in a family, the number of chocolates in a particular bag etc.

2) Continuous variables

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.A continuous random variable is not defined at specific values. Instead, it is defined over an interval of values

The random variables plays an important roles in any kind of studies or research as

-Random variables are needed because probability distributions are insufficient to describe realistic random phenomena.

-For practical problems its is easy to model realizations of random variables to work with,instead of probability distribution directly