exercise:B8ae3c5bfd: 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> A share of common stock in the Pilsdorff beer company has a price <math>Y_n</math> on the <math>n</math>th business day of the year. Finn observes that the price change <math>X_n = Y_{n + 1} - Y_n</math> appears to be a random variable with mean...") |
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A share of common stock in the Pilsdorff beer company has a price <math>Y_n</math> on the <math>n</math>th business day of the year. Finn observes that the price change <math>X_n = Y_{n + 1} - Y_n</math> appears to be a random variable with mean | |||
has a price <math>Y_n</math> on the <math>n</math>th business day of the year. Finn observes that the | |||
price change <math>X_n = Y_{n + 1} - Y_n</math> appears to be a random variable with mean | |||
<math>\mu = 0</math> and variance <math>\sigma^2 =1/4</math>. If <math>Y_1 = 30</math>, find a lower bound for | <math>\mu = 0</math> and variance <math>\sigma^2 =1/4</math>. If <math>Y_1 = 30</math>, find a lower bound for | ||
the following probabilities, under the assumption that the <math>X_n</math>'s are mutually independent. | the following probabilities, under the assumption that the <math>X_n</math>'s are mutually independent. | ||
<ul><li> <math>P(25 \leq Y_2 \leq 35)</math>. | <ul style="list-style-type:lower-alpha"><li> <math>P(25 \leq Y_2 \leq 35)</math>. | ||
</li> | </li> | ||
<li> <math>P(25 \leq Y_{11} \leq 35)</math>. | <li> <math>P(25 \leq Y_{11} \leq 35)</math>. | ||
Latest revision as of 23:50, 14 June 2024
A share of common stock in the Pilsdorff beer company has a price [math]Y_n[/math] on the [math]n[/math]th business day of the year. Finn observes that the price change [math]X_n = Y_{n + 1} - Y_n[/math] appears to be a random variable with mean [math]\mu = 0[/math] and variance [math]\sigma^2 =1/4[/math]. If [math]Y_1 = 30[/math], find a lower bound for the following probabilities, under the assumption that the [math]X_n[/math]'s are mutually independent.
- [math]P(25 \leq Y_2 \leq 35)[/math].
- [math]P(25 \leq Y_{11} \leq 35)[/math].
- [math]P(25 \leq Y_{101} \leq 35)[/math].