Question

Explain the difference between a discrete and a continuous random variable.

Answer 1

Discrete Random Variable takes some isolated values. For example, number of letters in words, number of members in a family etc.
Whereas Continuous random variable takes any value within the range of variation. For example height, weight

discrete variable is one that can take countably infinitely many values
whereas a continuous random variable takes on uncountably infinitely many values.

Note:
For number of family members variable can never take fractional values such as 4.5 or 3.5. It won't make any sense.
But if the variable is height of a college student then the variable can take any value within 5 to 6 feet or more. It can take 5.5 or 5.677 (depending on the measurement we are using). We have no restrictions other than the range. So it can take any value within the given range

Discrete Random variable can also be called Discontinuous random variable.