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<h2 class="hd hd-2 unit-title">2.1 Descriptors of discrete random variables</h2>
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<h2 class="hd hd-2 unit-title">2.2 Descriptors of continuous random variables</h2>
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<h2 class="hd hd-2 unit-title">2.3 Normal distribution</h2>
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<h2 class="hd hd-2 unit-title">2.4 Lognormal distribution</h2>
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<h2 class="hd hd-2 unit-title">2.5 Correlation coefficient</h2>
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<h2 class="hd hd-2 unit-title">2.6Multivariate normal distribution</h2>
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<h2 class="hd hd-2 unit-title">Chapter 2 Homework</h2>
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<p style="margin: 0in; text-align: justify; text-justify: inter-ideograph;"><b><span style="font-family: 'Times New Roman',serif;">Problem: </span></b><span style="font-family: 'Times New Roman',serif;">Consider the following measurements about the cohesion of a soil: <o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent: 24.0pt;">12 kPa, 14 kPa, 18 kPa, 15 kPa, 16.2 kPa, 17. 6 kPa, 13 kPa<o:p></o:p></p>
<p style="margin: 0in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: 'Times New Roman',serif;">Work out the solutions of the following two problems, assuming the cohesion follows the normal and lognormal distributions, respectively,<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left: 21.0pt; text-indent: -21.0pt; mso-char-indent-count: 0; mso-list: l0 level1 lfo1;"><a name="_Hlk39838400"></a><!-- [if !supportLists]--><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman';"><span style="mso-list: Ignore;">1)<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><!--[endif]--><span style="font-family: 'Times New Roman',serif;">Draw the PDF of the cohesion;<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left: 21.0pt; text-indent: -21.0pt; mso-char-indent-count: 0; mso-list: l0 level1 lfo1;"><!-- [if !supportLists]--><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman';"><span style="mso-list: Ignore;">2)<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><!--[endif]--><span style="font-family: 'Times New Roman',serif;">Evaluate the probability that the cohesion is less than 5 kPa, 10 kPa, and 15 kPa.<o:p></o:p></span></p>
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