Random variables

Chapter 3

Discrete random variables and probability distributions

Random variables

Suppose that experiment of rolling two fair dice to be carried out.

Let X be the sum of outcomes, then X can only assume the values

2, 3, 4, ……., 12 with the following probabilities:

and so on.

The numerical value of random variable depends on the outcomes of the experiment. In this example, for instance, if it is (3, 2), then X is 5, and if it is (6, 6) then X is 12. In this example X is called a random variable.

Definition:

A random variable is a variable whose value is determined by the outcome of a random experiment.

Notationally, we use capital letters, such as X, to denote the random variable and corresponding lowercase x to denote a possible value.

Set of possible values of a random variable might be finite, infinite and countable, or uncountable.

Definition:

A random variable X is called a discrete random variable if it can take on no more than a countable number of values.

Some examples of discrete random variable:

1. The number of employees working at a company.

2. The number of heads obtained in three tosses of a coin.

3. The number of customers visiting a bank during any given day.

A random variable whose values are not countable is called a continuous random variable.

Definition:

A random variable X is called a continuous if it can take any value in an interval.

Here are some examples of continuous random variables:

1. Prices of houses

2. The amount of oil imported.

3. Time taken by workers to learn a job.

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