Revision as of 02:22, 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>?")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
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]]

?