exercise:47a991073c: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> <ul><li> A die is rolled three times with outcomes <math>X_1</math>, <math>X_2</math>, and <math>X_3</math>. Let <math>Y_3</math> be the maximum of the values obtained. Show that <math display="block"> P(Y_3 \leq j) = P(X_1 \leq j)^3\ . </math...") |
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< | <ul style="list-style-type:lower-alpha"><li> A die is rolled three times with outcomes <math>X_1</math>, <math>X_2</math>, and <math>X_3</math>. Let | ||
<math>Y_3</math> be the maximum of the values obtained. Show that | <math>Y_3</math> be the maximum of the values obtained. Show that | ||
Latest revision as of 23:59, 24 June 2024
- A die is rolled three times with outcomes [math]X_1[/math], [math]X_2[/math], and [math]X_3[/math]. Let
[math]Y_3[/math] be the maximum of the values obtained. Show that
[[math]] P(Y_3 \leq j) = P(X_1 \leq j)^3\ . [[/math]]Use this to find the distribution of [math]Y_3[/math]. Does [math]Y_3[/math] have a bell-shaped distribution?
- Now let [math]Y_n[/math] be the maximum value when [math]n[/math] dice are rolled. Find the distribution of [math]Y_n[/math]. Is this distribution bell-shaped for large values of [math]n[/math]?