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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> 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...") |
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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 | |||
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. | = 1</math>. Suppose there are <math>10^{20}</math> particles in the tube. | ||
<ul><li> Find the mean and variance of the average velocity of the particles. | <ul style="list-style-type:lower-alpha"><li> Find the mean and variance of the average velocity of the particles. | ||
</li> | </li> | ||
<li> What is the probability that the average velocity is <math>{} \geq | <li> What is the probability that the average velocity is <math>{} \geq | ||
Latest revision as of 23:31, 14 June 2024
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?