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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If two events, A and B, are not independent, then the joint probability of event A and event B equals a. the conditional probability of event A given event B times the marginal probability of the event B b. the conditional probability of event B given event A times the marginal probability of the event A c. both of the above d. none of the above
4. The odds that an event, A, happens is defined to be O(A) P(A) 1- P(A) If the odds that event A occurs is 3.0, what is the probability it happens? (a) (b) = If the odds that event A occurs is 3:0, what is the probability it happens? 3.0'
5. Suppose that you know that your friend was born sometime in the year 2001, but not which day. Given this state of ignorance, we can model your friend's birthday as being chosen uniformly at random from the 365 days of a non-leap year. (In reality, these are not entirely uniform, but they're pretty close, and we can ignore this effect.) (a) What is the probability that your friend was born in January? (b) Suppose you remember that your friend's birthday is on the 20th (of some month). Conditioned on this fact, what is the probability that your friend was born in January? (c) Now suppose you remember that your friend's birthday is on the 30th (of soe month). Conditioned on this fact, what is the probability that your friend was born in January?
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.
V. (10) The following table of 850 students shows those that have or don't have covid-19 and shows those who had a positive test or a negative test. I just made this data up so don't take this as representative of our current state. Answer the following questions. Negative Test 5 Positive Test Have Covid-19 45 Don't have Covid-19 25 775 Let D be the event you Don't have Covid-19 and N the event you have a negative test. 1. P(D) = 2. P(D I N) = 3. Are D and N independent? 5. What is the probability that you Have Covid-19 even though the test came back negative? 4. Explain TI-84 Plus TEXAS INSTRUMENTS
3. A coin is tossed repeatedly, heads occurring on each toss with probability p. Find the probability generating function of the number T of tosses before a run of n heads has appeared for the first time.
11. The probability that Adam goes to play basketball on any day is 3/3.3 5 a day when he plays basketball, the probability that Adam has burgers 3 is On the day he does not play basketball, the probability he has 8 burgers 3 11 (a) Find probability that Adam has burgers on any day. (b) Adam has burgers on that day. What is the probability he plays basketball? On (c) Determine whether the events play and does not play basketball mutually exclusive. (d) Determine whether the events play basketball and has burgers independent.
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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