EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6, Problem 6.9STPE
Consider a directory of classified advertisements that consists of m pages, where m is very large. Suppose that the number of advertisements per page varies and that your only method of finding out how many advertisements there are on a specified page is to count them. In addition, suppose that there are too many pages for it to be feasible to make a complete count of the total number of advertisements and that your objective is to choose a directory advertisement in such a way that each of them has an equal chance of being selected.
a. If you randomly choose a page and then randomly choose an advertisement from that page, would that satisfy your objective? Why or why not?
Let
Step 1. Choose a page at random. Suppose it is page X. Determine n(X) by counting the number of advertisements on page X.
Step 2. “Accept” page X with
Step 3. Randomly choose one of the advertisements on page X.
Call each pass of the algorithm through step 1 an iteration. For instance, if the first randomly chosen page is rejected and the second accepted, then we would have needed 2 iterations of the algorithm to obtain an advertisement.
b. What is the probability that a single iteration of the algorithm results in the acceptance of an advertisement on page i?
c. What is the probability that a single iteration of the algorithm results in the acceptance of an advertisement?
d. What is the probability that the algorithm goes through k iterations, accepting the jth advertisement on page i on the final iteration?
e. What is the probability that the jth advertisement on page i is the advertisement obtained from the algorithm?
f. What is the expected number of iterations taken by the algorithm?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Suppose Laura, a facilities manager at a health and wellness company, wants to estimate the difference in the average amount of time that men and women spend at the company's fitness centers each week.
Laura randomly selects 15 adult male fitness center members from the membership database and then selects 15 adult female members from the database. Laura gathers data from the past month containing logged time at the fitness center for these members. She plans to use the data to estimate the difference in the time men and women spend per week at the fitness center. The sample statistics are summarized in the table.
Population
Populationdescription
Population mean(unknown)
Samplesize
Sample mean(min)
Sample standarddeviation (min)
11
male
μ1
n=15
x¯1=137.7
s=51.7
22
female
μ2
n=15
x¯2=114.6
s=34.2
df=24.283
The population standard deviations are unknown and unlikely to be equal, based on the sample data. Laura plans to use the two-sample ?-t-procedures to estimate the…
Workers in Company XYZ used 200 computers for their daily operation. In that company, the computers are categorized into type A and B. The workers usually complained that they experience performance problems with the computers more than once per week. Based on a survey, the company found that fifty of the Type A computers will encounter problems more than once per week. Meanwhile seventy-five of the Type B computers do not experience problems more than once per week. There are 120 Type B computers in the company.
Based on the above scenario determined whether the events “Type A computer” and “experience problems more than once per week” are independent event? Explain.
do number 2 need it fast!!
Chapter 6 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 6 - Two fair dice are rolled. Find the joint...Ch. 6 - Suppose that 3 balls are chosen without...Ch. 6 - In Problem 8 t, suppose that the white balls are...Ch. 6 - Repeat Problem 6.2 when the ball selected is...Ch. 6 - Repeat Problem 6.3a when the ball selected is...Ch. 6 - The severity of a certain cancer is designated by...Ch. 6 - Consider a sequence of independent Bernoulli...Ch. 6 - Prob. 6.8PCh. 6 - The joint probability density function of X and Y...Ch. 6 - Prob. 6.10P
Ch. 6 - In Example Id, verify that f(x,y)=2exe2y,0x,0y, is...Ch. 6 - The number of people who enter a drugstore in a...Ch. 6 - A man and a woman agree to meet at a certain...Ch. 6 - An ambulance travels back and forth at a constant...Ch. 6 - The random vector (X,Y) is said to be uniformly...Ch. 6 - Suppose that n points are independently chosen at...Ch. 6 - Prob. 6.17PCh. 6 - Let X1 and X2 be independent binomial random...Ch. 6 - Show that f(x,y)=1x, 0yx1 is a joint density...Ch. 6 - Prob. 6.20PCh. 6 - Let f(x,y)=24xy0x1,0y1,0x+y1 and let it equal 0...Ch. 6 - The joint density function of X and Y is...Ch. 6 - Prob. 6.23PCh. 6 - Consider independent trials, each of which results...Ch. 6 - Suppose that 106 people arrive at a service...Ch. 6 - Prob. 6.26PCh. 6 - Prob. 6.27PCh. 6 - The time that it takes to service a car is an...Ch. 6 - The gross daily sales at a certain restaurant are...Ch. 6 - Jills bowling scores are approximately normally...Ch. 6 - According to the U.S. National Center for Health...Ch. 6 - Monthly sales are independent normal random...Ch. 6 - Let X1 and X2 be independent normal random...Ch. 6 - Prob. 6.34PCh. 6 - Teams 1, 2, 3, 4 are all scheduled to play each of...Ch. 6 - Let X1,...,X10 be independent with the same...Ch. 6 - The expected number of typographical errors on a...Ch. 6 - The monthly worldwide average number of airplane...Ch. 6 - In Problem 6.4, calculate the conditional...Ch. 6 - In Problem 6.3 calculate the conditional...Ch. 6 - Prob. 6.41PCh. 6 - Prob. 6.42PCh. 6 - Prob. 6.43PCh. 6 - The joint probability mass function of X and Y is...Ch. 6 - Prob. 6.45PCh. 6 - Prob. 6.46PCh. 6 - An insurance company supposes that each person has...Ch. 6 - If X1,X2,X3 are independent random variables that...Ch. 6 - Prob. 6.49PCh. 6 - If 3 trucks break down at points randomly...Ch. 6 - Consider a sample of size 5 from a uniform...Ch. 6 - Prob. 6.52PCh. 6 - Let X(1),X(2),...,X(n) be the order statistics of...Ch. 6 - Let Z1 and Z2 be independent standard normal...Ch. 6 - Derive the distribution of the range of a sample...Ch. 6 - Let X and Y denote the coordinates of a point...Ch. 6 - Prob. 6.57PCh. 6 - Prob. 6.58PCh. 6 - Prob. 6.59PCh. 6 - Prob. 6.60PCh. 6 - Repeat Problem 6.60 when X and Y are independent...Ch. 6 - Prob. 6.62PCh. 6 - Prob. 6.63PCh. 6 - In Example 8b, let Yk+1=n+1i=1kYi. Show that...Ch. 6 - Consider an urn containing n balls numbered 1.. .....Ch. 6 - Suppose X,Y have a joint distribution function...Ch. 6 - Prob. 6.2TECh. 6 - Prob. 6.3TECh. 6 - Solve Buffons needle problem when LD.Ch. 6 - If X and Y are independent continuous positive...Ch. 6 - Prob. 6.6TECh. 6 - Prob. 6.7TECh. 6 - Let X and Y be independent continuous random...Ch. 6 - Let X1,...,Xn be independent exponential random...Ch. 6 - The lifetimes of batteries are independent...Ch. 6 - Prob. 6.11TECh. 6 - Show that the jointly continuous (discrete) random...Ch. 6 - In Example 5e t, we computed the conditional...Ch. 6 - Suppose that X and Y are independent geometric...Ch. 6 - Consider a sequence of independent trials, with...Ch. 6 - If X and Y are independent binomial random...Ch. 6 - Suppose that Xi,i=1,2,3 are independent Poisson...Ch. 6 - Prob. 6.18TECh. 6 - Let X1,X2,X3 be independent and identically...Ch. 6 - Prob. 6.20TECh. 6 - Suppose that W, the amount of moisture in the air...Ch. 6 - Let W be a gamma random variable with parameters...Ch. 6 - A rectangular array of mn numbers arranged in n...Ch. 6 - If X is exponential with rate , find...Ch. 6 - Suppose thatF(x) is a cumulative distribution...Ch. 6 - Show that if n people are distributed at random...Ch. 6 - Suppose that X1,...,Xn are independent exponential...Ch. 6 - Establish Equation (6.2) by differentiating...Ch. 6 - Show that the median of a sample of size 2n+1 from...Ch. 6 - Prob. 6.30TECh. 6 - Compute the density of the range of a sample of...Ch. 6 - Let X(1)X(2)...X(n) be the ordered values of n...Ch. 6 - Let X1,...,Xn be a set of independent and...Ch. 6 - Let X1,....Xn, be independent and identically...Ch. 6 - Prob. 6.35TECh. 6 - Prob. 6.36TECh. 6 - Suppose that (X,Y) has a bivariate normal...Ch. 6 - Suppose that X has a beta distribution with...Ch. 6 - 6.39. Consider an experiment with n possible...Ch. 6 - Prob. 6.40TECh. 6 - Prob. 6.41TECh. 6 - Each throw of an unfair die lands on each of the...Ch. 6 - The joint probability mass function of the random...Ch. 6 - Prob. 6.3STPECh. 6 - Let r=r1+...+rk, where all ri are positive...Ch. 6 - Suppose that X, Y, and Z are independent random...Ch. 6 - Let X and Y be continuous random variables with...Ch. 6 - The joint density function of X and Y...Ch. 6 - Consider two components and three types of shocks....Ch. 6 - Consider a directory of classified advertisements...Ch. 6 - The random parts of the algorithm in Self-Test...Ch. 6 - Prob. 6.11STPECh. 6 - The accompanying dartboard is a square whose sides...Ch. 6 - A model proposed for NBA basketball supposes that...Ch. 6 - Let N be a geometric random variable with...Ch. 6 - Prob. 6.15STPECh. 6 - You and three other people are to place bids for...Ch. 6 - Find the probability that X1,X2,...,Xn is a...Ch. 6 - 6.18. Let 4VH and Y, be independent random...Ch. 6 - Let Z1,Z2.....Zn be independent standard normal...Ch. 6 - Let X1,X2,... be a sequence of independent and...Ch. 6 - Prove the identity P{Xs,Yt}=P{Xs}+P{Yt}+P{Xs,Yt}1...Ch. 6 - In Example 1c, find P(Xr=i,Ys=j) when ji.Ch. 6 - A Pareto random variable X with parameters a0,0...Ch. 6 - Prob. 6.24STPECh. 6 - Prob. 6.25STPECh. 6 - Let X1,...,Xn, be independent nonnegative integer...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- RVW (Restored Volkswagens) buys 15 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 10 each to three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below. a. Given the costs below, draw a network representation for this problem. Repair Shops Used Car Lots S1 S2 L1 L2 L3 Auction 1 460 520 S1 250 300 500 Auction 2 450 500 S2 300 550 450 b. Formulate this problem as a transshipment…arrow_forwardWithin a group of 12 women, there are five who have known each other for a long time and have an excellent relationship. The other 7 women do not know the 5 friends nor do they know each other. Whenever a subset of the five friends is equal to or greater than 50% of the number of people in another work group (for example, if there are two of the five friends in the work group of three or four people), then the group work becomes high performance It is desired to form a working group by selecting five women from the 12 women. What is the probability that the work group is high performing? Please indicate your answer in the space provided below as a number between zero and one, to four decimal places.arrow_forwardA psychologist at the Royal Ottawa Hospital was asked to determine whether there was any clear difference in the length of stay (in days) of patients with different categories of diagnosis. The hospital was looking for ways to reduce costs and free up some more beds so that they could treat more patients from the community. They chose three diagnostic categories that they thought were possibly staying the longest and selected the 4 more recent admissions from each of these diagnostic categories: affective disorders, cognitive disorders, and drug-related disorders. The results are presented in Table 3 below. Using an alpha = .05 and showing all the steps of hypothesis testing, is there a significant difference in length of stay among diagnosistic categories? -do not use excel use formulasarrow_forward
- Consider there are only two computer companies in a country. The companies are named “Dude” and “Imac”. Each year, company Dude keeps 1/5th of its customers, while the rest switch to Imac. Each year, Imac keeps 1/3rd of its customers, while the rest switch to Dude. If in 2002, Dude has 1/6th of the market and Imac has 5/6th of the market, what is the distribution of the market share between the two companies in 2003. (Hint: you can cast this as a matrix multiplication problem)arrow_forwardThe sales manager of a large automotive parts distributor wants to estimate the total annual sales for each of the company’s regions. Five factors appear to be related to regional sales: the number of retail outlets in the region, the number of automobiles in the region registered as of April 1, the total personal income recorded in the first quarter of the year, the average age of the automobiles (years), and the number of sales supervisors in the region. The data for each region were gathered for last year. For example, see the following table. In region 1 there were 1,739 retail outlets stocking the company’s automotive parts, there were 9,270,000 registered automobiles in the region as of April 1, and so on. The region’s sales for that year were $37,702,000. constant outlet automobile reg income age bosses 37.702 1,739 9.27 85.4 3.5 9 24.196 1,221 5.86 60.7 5 5 32.055 1,846 8.81 68.1 4.4 7 3.611 120 3.81 20.2 4 5 17.625 1,096 10.31 33.8 3.5 7 45.919 2,290 11.62 95.1…arrow_forwardAJ’s sleep pattern had been fluctuating due to stress and diet, so he started to keep a diary of how many hours he slept each night. On the 4th night after he started the diary, AJ slept 9.4 hours, which was the most sleep he got any night. Gradually, he got less sleep each successive night until, on the 18th night after he started the diary, AJ slept 6.2 hours, which was the least sleep he got any night. After keeping his diary for 6 months, he realized that the number of hours he got each night followed a sinusoidal curve. Let t be the number of nights since he started his diary, and s be how many hours he slept that night. It may be helpful to draw a crude sketch of the sleep time function and label the known t − and s − values on it. POSITIVE or NEGATIVE SIN or COS Maximum s − value = Minimum s − value = ______________ ______________ Middle s − value = ______________ = D Amplitude = ______________ = A ⇒ B = ______________ Given the crude sketch of the height function, the…arrow_forward
- In a certain city, only 2 newspapers A and B are published. It is known that 25% of the city population read A and 20% read B while 8% reads both A and B. It is also known that 30% of those who read A but not B look into advertisement and 40% of those who read B but not A look into advertisements while 50% of those who read both A and B look into advertisements. What is the percentage of the population who read an advertisement?arrow_forwardconsidered a data 1,3,5,7,9,11,13,15,17,19,21,......81. how many iteration are required in linear searcharrow_forwardIn the city of AZ, there are two supermarkets, X-Mart and Y-Mart. It is assumed that every shopper makes a purchase once a week at one of these supermarkets (not both).In a study, 100 samples of shoppers were taken over 10 weeks. From the study, it is known that if a shopper goes to X-Mart in one week, 85 people will continue to shop at X-Mart in the following week, and if a shopper goes to Y-Mart in one week, 70 people will continue to shop at Y-Mart in the following week.Create a transition probability table and matrix for this scenario, and then If in the first week Ivankov buys from X-Mart, what is the probability that Terry will buy from X-Mart in the third and fourth weeks?arrow_forward
- conditions of both the districts with reference to these two causes of death. Assume The following are the information about the number of persons who are affected by Diabetes and Lung Cancer and the number of persons died due to Find the 1llness specific death rates for the two districts. Also, compare health District A District B No. of Persons No. of Persons Cause of Death Affected Died Affected Died 20000 325 22000 400 Diabetes 19500 300 21225 380 Lung Cancer la person affected by Diabetes is not affected by Lung Cancer and vice-versa.arrow_forwardWe need to assign 4 students (Daniel, Jeremy, Xiaoying, Ashu) to 3 different teams (Team 1, Team 2, and Team 3). Each team needs to have at least 1 student. To maximize productivity, it has been determined that Ashu and Jeremy cannot be on the same team. How many different ways are there to assign the teams?arrow_forwardSuppose Martin is a very talented used-car salesman. Whenever Martin talks to a new customer, there is a 90% chance that he convinces the customer to purchase one of his used cars. Brian, Martin's boss, is envious that Martin sells many more cars than he does. Because of his jealousy, Brian institutes a new rule that Martin is only allowed to talk to 35 customers per day. Thus, Martin continues to work each day until he speaks to 35 customers, at which point Brian sends him home. Let ? represent the number of used cars that Martin sells on a given day. What are the mean, ?, and variance, ?^2, of ?? Please round your answers to the nearest two decimal places. ?=_______? ?^2=_________?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License