# How are continuous and discrete treated differently?

A random variable is said to be discrete if the set of values assigned to the random variable is countable. Further, for every single value of the random variable, there is an associated probability. Hence to derive the constants of the discrete random variable, we use $\sum$.
The set of values assigned to a continuous random variable is uncountable. The probability is obtained for a range (interval) of values and not for individual values. Hence, to find the constants, we use $\int$.