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<h2 class="hd hd-2 unit-title">Gallery of continuous random variables</h2>
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<h2 class="hd hd-2 unit-title">Class 5 reading questions: 3</h2>
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Let [mathjaxinline]Z[/mathjaxinline] be a standard normal random variable. Use the R function <tt class="ttfamily">pnorm</tt> to compute each of the following. (Give 3 decimal places of accuracy.) </p>
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<p><b class="bf">(b)</b> [mathjaxinline]P(-1 &lt; Z &lt; 1)[/mathjaxinline]. </p>
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<h2 class="hd hd-2 unit-title">Manipulating random variables</h2>
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<h2 class="hd hd-2 unit-title">Class 5 reading questions: 4</h2>
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Suppose [mathjaxinline]X \sim \text {Uniform}(0,1)[/mathjaxinline] and [mathjaxinline]Y = X^3[/mathjaxinline]. In the range [0,1], the pdf for [mathjaxinline]Y[/mathjaxinline] is </p>
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(a) [mathjaxinline]3y^2[/mathjaxinline] &#8195;(b) [mathjaxinline]y^3[/mathjaxinline] &#8195;(c) [mathjaxinline]\frac43 y^{1/3}[/mathjaxinline] &#8195;(d) [mathjaxinline]\frac13 y^{-2/3}[/mathjaxinline] </p>
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