Continuous random variables: brief review

Random variables are introduced in the module Discrete probability distributions . Recall that a random variable is a variable whose value is determined by the outcome of a random procedure.

There are two main types of random variables: discrete and continuous. The modules Discrete probability distributions and Binomial distribution deal with discrete random variables, and the module Continuous probability distributions introduces continuous random variables and their distributions.

In this module, we study two specific continuous distributions, so we will be applying much of the theory developed in the module Continuous probability distributions .

A continuous random variable \(X\) can take any real value within a specified range. It has a probability density function (pdf) denoted by \(f_X(x)\) and a cumulative distribution function (cdf) denoted by \(F_X(x)\). Recall that

\[ \Pr(X \leq x) = F_X(x) = \int_{-\infty}^{x} f_X(t) \;dt, \]

for each real number \(x\).

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