Aug 01

Continuous versus discrete random variables (Quant: Stat)

by David Harper, CFA, FRM, CIPM

FRM |

Learning objective: Define random variables, and distinguish between continuous and discrete random variables

A distribution characterizes a random variable. The random variable can be discrete or continuous. Discrete random variables can be counted. Continuous random variables must be measured.

continuous_plots

In regard to the density function (as pictured above, not the cumulative function):

  • The density function of a discrete random variable is called a probability mass function (PMF)
  • The density function of a continuous random variable is called a probability density function (PDF)

Financial Risk Manager (FRM) Tip: All four of Gujarati’s “important probability distributions” are continuous: normal, student’s t, chi-square, and F distribution. They are all PDFs (not PMFs).

Continuous Discrete
Measured Counted
Infinite Finite
   
Time Binomial
Asset returns Poisson
Distance Logarithmic
Normal  
Student’s t  
chi-square  
Lognormal  

Comments

  1. Be the first to leave a comment!

Leave a Comment