Revision as of 02:19, 9 June 2024 by Bot (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> Let <math>x</math> and <math>y</math> be chosen at random from the interval <math>[0,1]</math>. Which pairs of the following events are independent? <ul><li> <math>x > 1/3</math>. </li> <li> <math>y > 2/3</math>. </li> <li> <math>x > y</mat...")
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BBy Bot
Jun 09'24

Exercise

[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]

Let [math]x[/math] and [math]y[/math] be chosen at random from the interval [math][0,1][/math]. Which

pairs of the following events are independent?

  • [math]x \gt 1/3[/math].
  • [math]y \gt 2/3[/math].
  • [math]x \gt y[/math].
  • [math]x + y \lt 1[/math].