What are the properties of (i) discrete random variable and (ii) continuous random variable?

Discrete random variable.

Continuous random variable.

Discrete random variable A variable which can assume finite number of possible values or an infinite sequence of countable real numbers is called a discrete random variable. Examples of discrete random variable: Marks obtained in a test. Number of red marbles in a jar. Number of telephone calls at a particular time. Number of cars sold by a car dealer in one month, etc.,

Continuous random variable A random variable X which can take on any value (integral as well as fraction) in the interval is called continuous random variable. Examples of continuous random variable The amount of water in a 10 ounce bottle. The speed of a car. Electricity consumption in kilowatt hours. Height of people in a population. Weight of students in a class. The length of time taken by a truck driver to go from Chennai to Madurai, etc.