Probability and Statistics for Computer Scientists, 2nd Edition

Chapter 4

Continuous Distributions

Recall that any discrete distribution is concentrated on a finite or countable number of isolated values. Conversely, continuous variables can take any value of an interval, (a, b), (a, +∞), (−∞, +∞), etc. Various times like service time, installation time, download time, failure time, and also physical measurements like weight, height, distance, velocity, temperature, and connection speed are examples of continuous random variables.

4.1 Probability density

For all continuous variables, the probability mass function (pmf) is always equal to zero,1

$P(x)=0\text{ for all }x.$

As a result, the pmf does not carry any information about a random variable. Rather, we can use the cumulative distribution function (cdf) F