exercise:C4bd624e06: 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>X</math> be a random variable with cumulative distribution function </math> F(x) = \left \{ \begin{array}{ll} 0, & \mbox{if <math>x < 0</math>}, \\ \sin^2(\pi x/2), & \mbox{if <math>0 \leq x \le...") |
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Let <math>X</math> be a random variable with cumulative distribution function | |||
<math display="block"> | |||
< | |||
F(x) = \left \{ \begin{array}{ll} | F(x) = \left \{ \begin{array}{ll} | ||
0, & \mbox{if | 0, & \mbox{if $x < 0$}, \\ | ||
\sin^2(\pi x/2), & \mbox{if | \sin^2(\pi x/2), & \mbox{if $0 \leq x \leq 1$}, \\ | ||
1, & \mbox{if | 1, & \mbox{if $1 < x $}. | ||
\end{array} | \end{array} | ||
\right. | \right. | ||
<math | </math> | ||
<ul><li> What is the density function | <ul style="list-style-type:lower-alpha"><li> What is the density function <math>f_X</math> for <math>X</math>?</li> | ||
</li> | <li> What is the probability that <math>X < 1/4</math>?</li> | ||
<li> What is the probability that <math>X < 1/4</math>? | |||
</li> | |||
</ul> | </ul> | ||
Latest revision as of 00:07, 25 June 2024
Let [math]X[/math] be a random variable with cumulative distribution function
[[math]]
F(x) = \left \{ \begin{array}{ll}
0, & \mbox{if $x \lt 0$}, \\
\sin^2(\pi x/2), & \mbox{if $0 \leq x \leq 1$}, \\
1, & \mbox{if $1 \lt x $}.
\end{array}
\right.
[[/math]]
- What is the density function [math]f_X[/math] for [math]X[/math]?
- What is the probability that [math]X \lt 1/4[/math]?