i-0¹¹for a - 1, 2; but ₁0¹i < ∞ for d ≥ 3. By Theorem 2the drunkard's walk in certain recurrent in dimensions 1 and 2; but uncertainrecurrent in dimensions 3 and higher.Exercise 3. Much more is known about all this. Some things for you to researchand report on.What if the drunkard's walk is asymmetric? That is the probability of amove to the left is not the same as a move to the right?• For the symmetric walk, what is the value of the recurrence probability ford> 3?• In the case d = 1,2 what is the expected length of a path returning to theorigin?. In the case d = 1,2, what is the probability of two returns? Three returns?An infinity of returns to the origin?7

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Answered: • What if the drunkard's walk is…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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7. Suppose that there is 50% chance that it will rain today and 60% chance that it will rain tomorrow. Suppose also that there is 30% chance that it will rain both days. The probability that it either will rain today or tomorrow, but not both, is A. 0.5 B. 0.6 C. 0.3 D. 0.1
Events A and B are mutually exclusive. Suppose event A occurs with probability 0.48 and event B occurs with probability 0.42. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that A does not occur or B does not occur (or both). (b) Compute the probability that either B occurs without A occurring or A and B both occur.
Example 3 : A hospital switch board receives an aveage of 4 emergency calls in a 10 minute interval. What is the probability that (i) there are at most 2 emergency calls in a 10 minute interval (ii) there are exactly 3 emergency calls in a 10 minute interval.
13.) A string of Christmas lights contains 20 lights. The lights are wired in series, so that if any light fails, the whole string will go dark. Each light has probability 0.98 of working for a 3- year period. The lights fail independently of each other. Find the probability that the string of lights will remain bright for 3 years.
1. Event A occurs with probability 0.1. Event B occurs with probability 0.6. If A and B are independent, then (а) Р(А or B) %3D 0.70. (b) Р(А or B) 3 0.06. (c) P(A and B) = 0.06. (d) P(A and B) = 0.70.
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12. Bob and Alice enter an archery contest. Bob hits his target with probability p, 0< p<1, and Alice hits her target, independently of Bob, with probability q, 0
8 Suppose disease X can be passed from father to child. If a father has the disease, each child has a 1/2 chance of having it too (independent of whether any other children do). If a father doesn't have the disease, none of their children will. Alexei is a father, and there's a 1/4 chance he has disease X. What is the probability Alexei has disease X if he has 2 children and neither one has the disease?
3. I throw a sequence of 3 darts at a dartboard, aiming for the centre. Assume each one of my throws is equally skillful-that is, I don't have a tendency to gef better (or worse!) with each throw. Suppose my sec- ond throw is better than my first. What is the probability that my third throw will be better than my second? The next question is the one that really interests me: is this problem really the car goat goat problem in dis- guise? If so explain carefully why these two problems are really the same. If not, explain how they are dif- ferent.

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