Random variable that can take any value in some part of the real line (in an uncountable set)

is a normally distributed random variable

A continuous random variable can be transformed into a discrete random variable

If you know the probability density function (PDF) of a continuous random variable, then you can find the cumulative distibution function (CDF) by taking a derivative of the PDF.

Random variable with a finite number of possible values always has a finite expected value (i.e. )

Random variable with infinite countable set of possible values always has a finite expected value (i.e. )