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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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 | |||
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 00:26, 15 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].