<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="description">
    <name>
      <text>38.1.2.8 Important Continous Distributions</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<h5>Important Continous Distributions</h5><p>There are a number of continuous distributions which have important applications in engineering and science. The areas of application and a little of the history (where appropriate) of the more important and useful distributions will be discussed in the later quizzes. Among the most important continuous probability distributions are the following.</p>
<ol><li>The Uniform or Rectangular distribution, where the random variable \(X\) is restricted to a finite interval \([a, b]\) and \(f(x)\) has constant density often defined by a function of the form:
\[ f(x) = \begin{cases} \dfrac{1}{b-a} &amp; \text{for all $ a \leq&nbsp; x \leq b$} \\ \\ 0 &amp; \text{elsewhere} \end{cases}. \]</li> 
<li>The Exponential distribution defined by a probability density function of the form:
\[ f(t)= \lambda e ^{-\lambda t},\] \(\lambda\) is a given constant.<br></li>
<li>The Normal distribution (often called the Gaussian distribution) where the random variable \(X\) is defined by a probability density function of the form:
\[f(x) = \dfrac{1}{\sigma \sqrt{2\pi}} e^{-(x-\mu)^2/2\sigma^2},\] \(\sigma, \mu\) are given constants.</li>
<li>The Weibull distribution where the random variable \(X\) is defined by a probability density
function of the form: \[f(x)=\alpha \beta (\alpha x)^{\beta-1}e^{-(\alpha x)^{\beta}},\] \(\alpha, \beta\) are given constants.</li></ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text/>
    </generalfeedback>
    <defaultgrade>0</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
  </question>
</quiz>
