Random Variables

A random variable is a variable that takes on numerical values determined by the outcome of a random experiment.

It is important to distinguish between a random variable and the possible values that it can take. Notationally, this is done by using capital letters, such as X to denote the random variable and the corresponding lowercase letter, x, to denote a possible value. For example, prior to the results being observed in the throw of a die, we can use the random variable X to denote the outcome. This random variable can take the specific values x = 1, x = 2, ….., x = 6, each with probability P(X = 1)=……………P(X = 6) = 1/6

Discrete Random Variable

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

Some examples of discrete random variables are:

1.     The number of defective items in a sample of 20 items from a large shipment.

2.     The number customers arriving at a checkpoint counter in an hour.

3.     The number of errors detected in a corporation’s accounts.

4.     The number of claims on a medical insurance policy in a particular year.

Continuous Random Variable

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

For, continuous random variables we cannot assign probabilities to specific values. For example, the probability that today’s high temperature will be precisely 77.236 degree Fahrenheit is 0. The temperature will certainly not be precisely that figure. However, probabilities may be determined for ranges, so that one could attach a probability to the event “Today’s high temperature will be between 75 and 80 degree.”