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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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
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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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