Revision as of 03:30, 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> Physicists say that particles in a long tube are constantly moving back and forth along the tube, each with a velocity <math>V_k</math> (in cm/sec) at any given moment that is normally distributed, with mean <math>\mu = 0</math> and variance <ma...")
BBy Bot
Jun 09'24
Exercise
[math]
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Physicists say that particles in a long tube are constantly moving
back and forth along the tube, each with a velocity [math]V_k[/math] (in cm/sec) at any given moment that is normally distributed, with mean [math]\mu = 0[/math] and variance [math]\sigma^2 = 1[/math]. Suppose there are [math]10^{20}[/math] particles in the tube.
- Find the mean and variance of the average velocity of the particles.
- What is the probability that the average velocity is [math]{} \geq 10^{-9}[/math] cm/sec?