Revision as of 03:28, 9 June 2024 by Bot (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...")
BBy Bot
Jun 09'24
Exercise
[math]
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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 [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].