Q3)Consider an infinite-length path that consists of discrete segments. There is a person that ismoving on this path according to a simple rule: At each turn, the person throws a (possibly unfair)dice. Suppose the output of the dice is k, then the person jumps k segments ahead and proceedswith throwing the dice again. For instance, if the person is at the n-th segment and the outputof the dice is 3, the person jumps 3 segments and steps on the (n+3)-th segment. We do nothave any idea about the starting point of the person; assume that the person is coming from minusinfinity and going to plus infinitya) Suppose the dice is unfair, and the person always throws the same fixed k, k € {1, 2, 3, 4, 5, 6},with probability 1. You mark a distinct segment on the path (for example segment n, for somefixed constant n). What is the probability that the person steps on this segment? (Hint: yourresult must be in terms of k)b) Consider the setup in part (a) with a fair dice i.e. all outcomes are equally likely. What isthe probability that the person steps on this segment? (Hint: your result must not be in terms ofk. Think about the average speed of this person)

a) Suppose the person always throws the same fixed number k. The probability of landing on the…

Answered: Consider an infinite-length path that…

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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4. A college wants to investigate whether students perform better on mornings that they have hada nutritious breakfast compared to mornings that they have not.You randomly recruit 100 students and tell each of them to come to the lab in two different mornings:each morning they will be offered some breakfast and will take a test. Each student will receivethe light breakfast one time and the nutritious breakfast the other time (some will receive the lightbreakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score aftereating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. Thus we aredoing students nutritious breakfast scores minus the light breakfast scores. a. Construct a 95% confidence interval for the difference in the average score of students afterhaving a nutritious breakfast and the average score of…
This student never eats the same kind of food for 2 consecutive weeks. If she eats in a Korean restaurant one week, then she is four times as likely to have Turkish as French food the next week. If she eats in a Turkish restaurant one week, then she is equally likely to have Korean as French food the next week. If she eats in a French restaurant one week, then she is five times as likely to have Korean as Turkish food the next week. Assume that state 1 is Korean and that state 2 is Turkish, and state 3 is French. Find the transition matrix for this Markov process. ... ... P = ... ...
r+ w 6. (a) There are possible positions that the red balls could occupy in the ordering as they are drawn. Therefore, the probability that they will be in the first r positions is
Question 2: preferred programming language for 43 of the students is Python, while the remaining students prefer C++. Five students will be selected at random to form Team 1. Let X represent the number of sampled students from Team 1 that prefer Python. Sixty computer science students are participating in a hack-a-thon. Suppose the a) What is the probability that none of the students on Team 1 prefer C++? b) How many students on Team 1 can be expected to prefer Python?
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Alice has 10 balls (all different). First, she splits them into two piles; then she picks one of the piles with at least two elements,and splits it into two; she repeats this until each pile has only one element.(a) How many steps does this take?(b) Show that the number of different ways in which she can carry out this procedure is[Hint: Imagine the procedure backward.]
This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese restaurant one week, then she is five times as likely to have Greek as Italian food the next week. If she eats a Greek restaurant one week, then she is four times as likely to have Chinese as Italian food the next week. If she eats a Italian restaurant one week, then she is twice as likely to have Chinese as Greek food the next week. Assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian. Find the transition matrix for this Markov process. P = 出出曲

In a gambling game, I roll two dice and win $1 if the sum of my two rolls is largerthan 7. I lose $1 if the sum of my two rolls is smaller than 7. In any other cases, Idon’t lose or win anything. I am going to repeat this game 72 times. c) Now make a box model for the number of times I win, including the values onthe tickets, the number of repeats of each ticket, and how many draws we willmake with replacement from the box. The average of the tickets in the box from (c) is ___________ and the SD is___________.
Suppose we want to choose 5 objects, without replacement, from 9 distinct objects. (a) If the order of the choices is not taken into consideration, how many ways can this be done? (b) If the order of the choices is taken into consideration, how many ways can this be done?
Four salesmen play "odd man out" to see who pays for lunch. They each flip a coin, and if there is a salesman whose coin doesn't match the others he pays for lunch. To clarify, the "odd man" must get heads while the other three get tails OR he must get tails while the other three get heads. Of course, since it is possible for two men get heads and two men get tails, not all flips will result in finding an "odd man". If this occurs the salesmen would be forced to flip again. What is the probability that there is an "odd man" the first time they flip?
"Question 3 (MaC)". (i) John has 5 toy cars and 4 toy buses that are all different from each other. John arranges these 9 toys in a line. Find the number of possible arrangements if: (a) (a) the cars and buses are arranged alternately. (B) the buses are all next to each other. (b) John randomly chooses 4 toys to take on holiday with him. Find (a) in how many ways John can choose the 4 toys. (B) the probability that his choices will include both his favourite car and his favourite bus. | (ii) Consider the function f(x) = x" +1 (a) Evaluate lim x→® x* +1 (b) Find the stationary point of the curve y = f(x) and determine its nature. (c) Find the point(s) of inflection of the curve y = f(x). (d) Sketch the curve y = f(x) showing all the features found above. Using your graph, find all values of k for which the equation kx² = 1-k has exactly one solution. (e)

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