Continuous random variables


Continuous random variables

The definition is pretty straightforward:

A continuous random variable models the result of an experiment that takes continues values.


As I have already mentioned, this is not the mathematically precise definition of a random variable. Nevertheless, it is good enough for our purposes.

There are a few mathematical concepts that we need to introduce in order to play with continuous random variables. These are probability density functions, cumulative distribution functions, expectations and variances. We will build these concepts gradually.


Which of the following experiments can be modeled with a continuous random variable (True/False):

  • Drawing two cards at random from a well-shuffled deck.

  • Weighing a piece of steel.

  • The radius of a single lamination of the stator of an electric machine punched out of a sheet of steel.

  • Gauging the pressure of a gas.

  • Counting the number of particles hitting a Geiger counter probe in one second.