Determine whether the following value is a discrete random v

Determine whether the following value is a discrete random variable (A), continuous random variable(B) , or not a random variable. (C)

Is the square footage of a pool a discrete random variable (A), continuous random variable(B) , or not a random variable. (C)

Solution

Let us define the difference between discrete and continuous random variables:

Discrete:

A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) 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 number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor\'s surgery, the number of defective light bulbs in a box of ten.

Continuous:

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

Square footage of a pool can take infinite values. Hence it is a continuous random variable.

Hope this helps.Ask if you have doubts.