Revision as of 03:22, 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>U</math> be a uniformly distributed random variable on <math>[0,1]</math>. What is the probability that the equation </math> x^2 + 4Ux + 1 = 0 <math display="block"> has two distinct real roots $x_1$ and <math>x_2</math>?")
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]U[/math] be a uniformly distributed random variable on [math][0,1][/math].
What is the probability that the equation </math> x^2 + 4Ux + 1 = 0
[[math]]
has two distinct real roots $x_1$ and \ltmath\gtx_2[[/math]]
?