exercise:39697bce76: 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> A point <math>Y</math> is chosen at random from <math>[0,1]</math>. A second point <math>X</math> is then chosen from the interval <math>[0,Y]</math>. Find the density for <math>X</math>. '' Hint'': Calculate <math>f_{X|Y}</math> as in Exercise...") |
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A point <math>Y</math> is chosen at random from <math>[0,1]</math>. A second point <math>X</math> is then chosen from the interval <math>[0,Y]</math>. Find the density for <math>X</math>. '' Hint'': Calculate <math>f_{X|Y}</math> as in [[exercise:Cc5799edfb |Exercise]] and then use | |||
point <math>X</math> is then chosen from the interval <math>[0,Y]</math>. Find the density for <math>X</math>. '' Hint'': Calculate <math>f_{X|Y}</math> as in | |||
<math display="block"> | <math display="block"> | ||
Latest revision as of 21:48, 14 June 2024
A point [math]Y[/math] is chosen at random from [math][0,1][/math]. A second point [math]X[/math] is then chosen from the interval [math][0,Y][/math]. Find the density for [math]X[/math]. Hint: Calculate [math]f_{X|Y}[/math] as in Exercise and then use
[[math]]
f_X(x) = \int_x^1 f_{X|Y}(x|y) f_Y(y)\, dy\ .
[[/math]]
Can you also derive your result geometrically?