Q2Let vo v1 ... v5 be a path. We fix an integer i, 0

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Let vov1 ... V5 be a path. We fix an integer i, 0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Q2
Let vo v1 ... v5 be a path. We fix an integer i, 0 <i< 5.
Suppose that a person starts walking from Vị, and at every vertex
Vj, 0 < j< 5, with probability p continues to vj-1 and with
probability 1 - p continues to vi+1. Let A; be the event that the
person visits v5 before vo for the first time.
(1) Show that P(A;) = pP(A;-1) + (1 – p)F(A;+1), for 0 <
i < 5.
(2) Use (1) to compute P(A;), for p = 3, for every i E
{1,2, 3, 4}.
Q3
We connect 5 resistors in series, where the i-th resistor, for 0 <
i< 5, has the resistance R; = 2'-1 N and connect the ends to
al V battery. Compute the electric potential V (i) at a vertex v;
between the i-th and (i + 1)-st resistors for i = 1, 2, 3, 4, and
vertices at the ends for i = 0, 5. (We neglect the resistance of the
wire. Choosing the flow of the electric current in either direction
consistently with voltages is fine. )
Compare your answer to your answer to Q2 (2).

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