A particle starts from the origin and moves in a certaindirection for a distance 1₁. Then it changes its direction many times, making arandom walk: for a distance /2, then for a distance 13, and so forth. The trajectoryof the wandering particle consists thus of segments of lengths 1₁, 12,..., , thedirection of each being determined by the angle ak made with the Ox-axis.These angles are uniformly distributed in the interval (0, 2), and they areindependent. Find the characteristic function of the coordinate X of the end-point of the trajectory and the corresponding probability density.

Answered: Image /qna-images/answer/65b50043-dc6e-495f-9ffe-1d28efeb5757.jpg

Answered: A particle starts from the origin and…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 22E

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