What is a random variable? What is an example of a discrete random variable and a continuous random variable?
Random Variable is a real valued function on the sample space, taking values on the real line (-∞,∞)
A random variable is a real number associated with the outcomes of a random experiment. eg. if a die is rolled and X denotes the number obtained on the die, then X is a random variable which can result in any of the following values 1,2,3,4,5 or 6, each with equal probability.
Discrete Random Variable: A random variable that assumes only a finite or countable number of possible values.
E.g. Marks obtained by a student in a test from 100 (the possibile marks would be from 0 to 100 and thus is countable)
It has a countable number of possible values.
Continuous Random Variable: A random variable that can assume an infinite and uncountable set of values.
E.g. Height of students in a class, Time it takes to travel from one point to another
It can take all values in a given interval of numbers.
Here we usually mean any value within a particular interval and not at a point.
Discrete Random Variables represent counted data and Continuous Random Variables represent measured data.