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      <text>38.1.1.1 Continuous probability distributions</text>
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      <text><![CDATA[<h3>Continuous probability distributions</h3>
<p>In order to get a good understanding of continuous probability distributions it is advisable to start by answering some fairly obvious questions such as: ''What is a continuous random variable?'',''Is there any carry over from the work we have already done on discrete random variables and distributions?'' We shall start with some basic concepts and definitions.</p>
<h5>Continuous random variables</h5>
<p>In day-to-day situations met by practising engineers, experiments such as measuring current in a
piece of wire or measuring the dimensions of machined components play a part. However closely an
engineer tries to control an experiment, there will always be small variations in the results obtained
due to many factors: the influence of factors outside the control of the engineer. Such influences
include changes in ambient temperature which may affect the accuracy of measuring devices used, and slight variation in the chemical composition of the materials used to produce the objects (wire,
machined components in this case) under investigation. In the case of machined components, many
of the small variations seen in measurements may be due to the influence of vibration, cutting tool
wear in the machine producing the component, changes in raw material used and the process used
to refine it, and even the measurement process itself!</p>
<p>Such variations (current and length for example) can be represented by a <b>random variable</b> and it is
customary to define an <b>interval</b>, finite or infinite, within which variation can take place. Since such
a variable (\(X\) say) can assume any value within an interval, we say that the variable is <b>continuous
</b>rather than discrete. - its values form an entity we can think of as a continuum.
The following definition summarizes the situation. </p>
<h5>Definition</h5>
<p>A random variable \(X\) is said to be continuous if it can assume any value in a given interval. This
contrasts with the definition of a discrete random variable which can only assume discrete values.
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