Continuous Probability Distributions - Types and Properties


Continuous Probability Distributions

Financial Risk Manager (FRM®) Part I of the FRM Exam covers the fundamental tools and techniques used in risk management and the theories that underlie their use.

Continuous Probability Distributions

In this session, we will learn mainly about the different types of continuous probability distributions. We will start by learning about the key properties of various continuous probability distributions and then we will move on to discuss the differences between them. Continuous probability distribution is the distribution in which the random variable of study is continuous in nature instead of discrete. The random variable takes all the values in a given range including all the real numbers.


We will discuss some of the continuous probability distributions such as normal distribution, log-normal distribution, beta distribution, gamma distribution, Weibull distribution, exponential distribution, logistic distribution, t-distribution, chi-squared distribution and extreme value distribution. GARP requires basic understanding of these distributions and their properties, and students are advised not to go in too much detail in terms of analytical interpretation and calculations. The distributions which are more important, such as normal distribution, student’s t-distribution and log-normal distribution have been discussed in extensive detail elsewhere in the FRM curriculum.

Normal Distribution

Starting off with Random Normal Distribution

Normal distribution is the type of continuous distribution that is most extensively used. It is bell-shaped and has a single peak at the center of the distribution.

Generally, finance-related random variables follow normal distribution, so knowledge about normal distribution is vital in understanding portfolio theory.

The normal curve falls off smoothly in either direction from the central value, which is the mean of the distribution. So the normal curve is symmetric.

It is completely described by its mean, ?, and its variance, σ2. The ? (mean) of the distribution is referred to as the location parameter, and the σ (standard deviation) measures how the distribution is spread out (known as the scale parameter).

The standard normal distribution has a mean of 0 and a standard deviation of 1.