exercise:242a63cd0b: 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 density function </math> f_X(x) = \left \{ \begin{array}{ll} cx(1 - x), & \mbox{if <math>0 < x < 1</math>}, \\ 0, & \mbox{otherwise.} \end{arra...") |
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Let <math>X</math> be a random variable with density function | |||
<math display="block"> | |||
< | |||
f_X(x) = \left \{ \begin{array}{ll} | f_X(x) = \left \{ \begin{array}{ll} | ||
cx(1 - x), & \mbox{if | cx(1 - x), & \mbox{if $0 < x < 1$}, \\ | ||
0, & \mbox{otherwise.} | 0, & \mbox{otherwise.} | ||
\end{array} | \end{array} | ||
\right. | \right. | ||
</math> | |||
< | <ul style="list-style-type:lower-alpha"><li> What is the value of <math>c</math>? | ||
</li> | </li> | ||
<li> What is the cumulative distribution function <math>F_X</math> for <math>X</math>? | <li> What is the cumulative distribution function <math>F_X</math> for <math>X</math>? | ||
Latest revision as of 10:10, 19 June 2024
Let [math]X[/math] be a random variable with density function
[[math]]
f_X(x) = \left \{ \begin{array}{ll}
cx(1 - x), & \mbox{if $0 \lt x \lt 1$}, \\
0, & \mbox{otherwise.}
\end{array}
\right.
[[/math]]
- What is the value of [math]c[/math]?
- What is the cumulative distribution function [math]F_X[/math] for [math]X[/math]?
- What is the probability that [math]X \lt 1/4[/math]?