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]
Using the notation introduced in Example, let
[[math]]
p_x = \left \{ \matrix{
\frac 23 \Bigl(\frac 13\Bigr)^k, & \mbox{if}\,\, x = 2^k, \cr
0, & \mbox{otherwise.}\cr
}\right.
[[/math]]
Show that there is exactly one value of [math]x[/math] such that if your envelope contains [math]x[/math], then you should switch.