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7. The motion of microscopic particles in a liquid or gas is irregular, because the particles collide with each other frequently. A model for this behaviour, called Brownian motion, is as follows: suppose that the particle is at the origin of a coordinate system at time t = 0, and let (X,Y, Z) denote the coordinates at time t. The random variables X, Y, Z are independent and normally distributed with mean 0 and variance o?t. What is the probability that at time t = 2 the particle will lie inside the sphere centered at the origin with radius 40?

7. The motion of microscopic particles in a liquid or gas is irregular, because the particles collide with each other frequently. A model for this behaviour, called Brownian motion, is as follows: suppose that the particle is at the origin of a coordinate system at time t = 0, and let (X,Y, Z) denote the coordinates at time t. The random variables X, Y, Z are independent and normally distributed with mean 0 and variance o?t. What is the probability that at time t = 2 the particle will lie inside the sphere centered at the origin with radius 40?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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The motion of microscopic particles in a liquid or gas is irregular, because the particles collide with each other frequently. A model for this behaviour, called Brownian motion, is as follows: suppose that the particle is at the origin of a coordinate system at time t = 0, and let (X,Y, Z) denote the coordinates at time t. The random variables X, Y, Z are independent and normally distributed with mean 0 and variance o?t. What is the probability that at time t = 2 the particle will lie inside the sphere centered at the origin with radius 40? 7.
Transcribed Image Text:The motion of microscopic particles in a liquid or gas is irregular, because the particles collide with each other frequently. A model for this behaviour, called Brownian motion, is as follows: suppose that the particle is at the origin of a coordinate system at time t = 0, and let (X,Y, Z) denote the coordinates at time t. The random variables X, Y, Z are independent and normally distributed with mean 0 and variance o?t. What is the probability that at time t = 2 the particle will lie inside the sphere centered at the origin with radius 40? 7.
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