exercise:5afdb5e440: 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> The price of one share of stock in the Pilsdorff Beer Company (see [[guide:Ee45340c30#sec 8.2 |Exercise.]]) is given by <math>Y_n</math> on the <math>n</math>th day of the year. Finn observes that the differences...")
 
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<div class="d-none"><math>
The price of one share of stock in the Pilsdorff Beer Company (see [[guide:Ee45340c30#sec 8.2 [[guide:Ee45340c30#exer 8.2.12 ||Exercise]].]]) is given by <math>Y_n</math> on the <math>n</math>th day of
\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> The price of one share of stock in the Pilsdorff Beer
Company (see [[guide:Ee45340c30#sec 8.2 [[guide:Ee45340c30#exer 8.2.12 ||Exercise]].]]) is given by <math>Y_n</math> on the <math>n</math>th day of
the year.  Finn observes that the differences <math>X_n = Y_{n + 1} - Y_n</math> appear to
the year.  Finn observes that the differences <math>X_n = Y_{n + 1} - Y_n</math> appear to
be independent random variables with a common distribution having mean <math>\mu =
be independent random variables with a common distribution having mean <math>\mu =
0</math> and variance <math>\sigma^2 = 1/4</math>.  If <math>Y_1 = 100</math>, estimate the probability
0</math> and variance <math>\sigma^2 = 1/4</math>.  If <math>Y_1 = 100</math>, estimate the probability
that <math>Y_{365}</math> is
that <math>Y_{365}</math> is
<ul><li>  <math>{} \geq 100</math>.
<ul style="list-style-type:lower-alpha"><li>  <math>{} \geq 100</math>.
</li>
</li>
<li>  <math>{} \geq 110</math>.
<li>  <math>{} \geq 110</math>.

Latest revision as of 23:26, 14 June 2024

The price of one share of stock in the Pilsdorff Beer Company (see [[guide:Ee45340c30#sec 8.2 |Exercise.]]) is given by [math]Y_n[/math] on the [math]n[/math]th day of the year. Finn observes that the differences [math]X_n = Y_{n + 1} - Y_n[/math] appear to be independent random variables with a common distribution having mean [math]\mu = 0[/math] and variance [math]\sigma^2 = 1/4[/math]. If [math]Y_1 = 100[/math], estimate the probability that [math]Y_{365}[/math] is

  • [math]{} \geq 100[/math].
  • [math]{} \geq 110[/math].
  • [math]{} \geq 120[/math].