## 3.1 Continuous random variables

Recall from Topic 1 that a continuous variable is one where *"the variable can take an infinite number of values within a certain range. For example, height, weight or age."* Consequentially, height, weight, and age are all examples of variables that are ** continuous random variables**.

Consider the following: let \(X\) denote the height in cm of university students. Considering the fact that a height cannot be negative, we could say that the possible values for \(X\) are in the range \((0, \infty)\). (\(\infty\) is a mathematical symbol that means 'infinity'.) A height could be any number within that range. It would be impossible to write down all of the potential values \(X\) could take, because \(X\) is a continuous random variable and can therefore take an infinite number of values within this range.

Recall that in Topic 2 we discussed the concepts of ** mean**,

**, and**

*variance***. These concepts can be related to a continuous random variable \(X\) as follows:**

*standard deviation***Expected value, variance and standard deviation of a random variable**

- The
(or*expected value*) of \(X\) can be denoted \(\text{E}(X) = \mu\)*mean* - The
of \(X\) can be denoted \(\text{Var}(X) = \sigma^2\)*variance* - The
of \(X\) is the square root of the variance and can be denoted \(\text{SD}(X) = \sqrt{\sigma^2} = \sigma\)*standard deviation*