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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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