exercise:95059a0f62: 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> 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>?") |
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Let <math>U</math> be a uniformly distributed random variable on <math>[0,1]</math>. | |||
What is the probability that the equation | What is the probability that the equation | ||
<math display = "block"> | |||
x^2 + 4Ux + 1 = 0 | |||
</math> | </math> | ||
has two distinct real roots <math>x_1</math> and <math>x_2</math>? | |||
has two distinct real roots | |||
Latest revision as of 02:12, 14 June 2024
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 [math]x_1[/math] and [math]x_2[/math]?