Published online by Cambridge University Press: 19 June 2025
This chapter introduces continuous random variables which enable us to model uncertain continuous quantities. We again begin with a formal definition, but quickly move on to describe how to manipulate continuous random variables in practice. We define the cumulative distribution function and quantiles (including the median) and explain how to estimate them from data. We then introduce the concept of probability density and describe its main properties. We present two approaches to obtain nonparametric models of probability densities from data: The histogram and kernel density estimation. Next, we define two celebrated continuous parametric distributions – the exponential and the Gaussian – and show how to fit them to data using maximum-likelihood estimation. We use these distributions to model the interarrival time of calls at a call center, and height in a population, respectively. Finally, we discuss how to simulate continuous random variables via inverse transform sampling.
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