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Consider a particle to be constrained to lie along a one-dimensional segment 0 to a. The probability that the particle is found to lie between x and x+dx is given by where n 1, 2, 3,.... = p(x)dx = 2 sin² (x)dx, 1) Show that p(x) is normalized. a 2) Calculate the average position of the particle along the line segment. 3) Calculate the variance, σ², associated with p(x). (1)

Consider a particle to be constrained to lie along a one-dimensional segment 0 to a. The probability that the particle is found to lie between x and x+dx is given by where n 1, 2, 3,.... = p(x)dx = 2 sin² (x)dx, 1) Show that p(x) is normalized. a 2) Calculate the average position of the particle along the line segment. 3) Calculate the variance, σ², associated with p(x). (1)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Consider a particle to be constrained to lie along a one-dimensional segment 0 to a. The probability that the particle is found to lie between x and x+dx is given by p(x)dx= = 2 - a sin² (n) da, (1) where n 1, 2, 3, . . . . = .. 1) Show that p(x) is normalized. 2) Calculate the average position of the particle along the line segment. 3) Calculate the variance, σ², associated with p(x).
Transcribed Image Text:Consider a particle to be constrained to lie along a one-dimensional segment 0 to a. The probability that the particle is found to lie between x and x+dx is given by p(x)dx= = 2 - a sin² (n) da, (1) where n 1, 2, 3, . . . . = .. 1) Show that p(x) is normalized. 2) Calculate the average position of the particle along the line segment. 3) Calculate the variance, σ², associated with p(x).
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