EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
Author: Ross
Publisher: VST
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 7, Problem 7.12STPE
(a)
To determine
To find:
The expected number of the given probability.
(b)
To determine
To find:
The variance of the number of the given probability.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
There are X-Mart and Y-Mart convenience stores. It is assumed that each customer purchases once a week at one of the two supermarkets (but not both). In a study, a sample of 100 buyers was taken for 10 weeks. From this research it is known that if buyers go to X-mart store one week, 85 people will still buy at X-mart store the following week and if buyers go to Y-mart store one week, 70 people will still buy at Y-mart store. mart the following week.
1. Make a table and matrix of transition probabilities.
2. If John purchases at X-mart in the first week, what is the probability that Bob purchases at X-store in the third and fourth weeks?
A student feels that 70% of her college courses have been enjoyable and the remainder have been boring. This student has access to student evaluations of professors and finds out that professors who had previously received strong positive evaluations from their students have taught 60% of his enjoyable courses and 25% of his boring courses. Next semester the student decides to take three courses, all from professors who have received strongly positive student evaluations. Assume that this student’s reactions to the three courses are independent of one another.a. What is the probability that this student will find all three courses enjoyable?b. What is the probability that this student will find at least one of the courses enjoyable?
When looking at the data for graduate school admissions between men and women, it is shown that about 45% of men are admitted but only 38% of women. However, when the data is broken down by school it turns out that, within each school, the women are admitted at higher rates than the men. This could happen because
I. The women apply in higher numbers to schools with lower acceptance rates.
II. The women apply in higher numbers to schools with higher acceptance rates
III. The men apply in higher numbers to schools with lower acceptance rates
IV. The men apply in higher numbers to schools with higher acceptance rates
Chapter 7 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 7 - A player throws a fair die and simultaneously...Ch. 7 - The game of Clue involves 6 suspects, 6 weapons,...Ch. 7 - Gambles are independent, and each one results in...Ch. 7 - Prob. 7.4PCh. 7 - The county hospital is located at the center of a...Ch. 7 - A fair die is rolled 10 times. Calculate the...Ch. 7 - Suppose that A and B each randomly and...Ch. 7 - N people arrive separately to a professional...Ch. 7 - A total of n. balls, numbered 1 through n, are put...Ch. 7 - Consider 3 trials, each having the same...
Ch. 7 - Consider n independent flips of a coin having...Ch. 7 - A group of n men and n women is lined up at...Ch. 7 - A set of 1000 cards numbered 1 through 1000 is...Ch. 7 - An urn has m black balls. At each stage, a black...Ch. 7 - In Example 2h, say that i and j, ij form a matched...Ch. 7 - Let Z be a standard normal random variable, and,...Ch. 7 - A deck of n cards numbered 1 through n is...Ch. 7 - Cards from an ordinary deck of 52 playing cards...Ch. 7 - Prob. 7.19PCh. 7 - Prob. 7.20PCh. 7 - For a group of 100 people, compute a. the expected...Ch. 7 - How many times would you expect to roll a fair die...Ch. 7 - Urn I contains 5 white and 6 black balls, while...Ch. 7 - A bottle initially contains m large pills and n...Ch. 7 - Let X1,X2... be a sequence of independent and...Ch. 7 - If X1,X2,....Xn are independent and identically...Ch. 7 - If 101 items are distributed among 10 boxes, then...Ch. 7 - Prob. 7.28PCh. 7 - There are 4 different types of coupons, the first...Ch. 7 - If X and Y are independent and identically...Ch. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - If E[X]=1 and Var(X)=5, find a. E[(2+X)2]: b....Ch. 7 - If 10 married couples are randomly seated at a...Ch. 7 - Cards from an ordinary deck are turned face up one...Ch. 7 - Let X be the number of ls and F the number of 2s...Ch. 7 - A die is rolled twice. Let X equal the sum of the...Ch. 7 - Suppose X and Y have the following joint...Ch. 7 - Suppose that 2 balls are randomly removed from an...Ch. 7 - Prob. 7.40PCh. 7 - Let X1,... be independent with common mean and...Ch. 7 - Prob. 7.42PCh. 7 - A pond contains 100 fish, of which 30 are carp. If...Ch. 7 - A group of 20 people consisting of 10 men and 10...Ch. 7 - Let X1,X2,...,Xn be independent random variables...Ch. 7 - Between two distinct methods for manufacturing...Ch. 7 - Prob. 7.47PCh. 7 - Consider the following dice game. as played at a...Ch. 7 - Prob. 7.49PCh. 7 - A fair die is successively rolled. Let X and Y...Ch. 7 - There are two misshapen coins in a box; their...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - A population is made up of r disjoint subgroups....Ch. 7 - A prisoner is trapped in a cell containing 3...Ch. 7 - Consider the following dice game: A pair of dice...Ch. 7 - Ten hunters are waiting for ducks to fly by. When...Ch. 7 - The number of people who enter an elevator on the...Ch. 7 - Suppose that the expected number of accidents per...Ch. 7 - A coin having probability p of coming up heads is...Ch. 7 - A coin that comes up heads with probability p is...Ch. 7 - There are n+1 participants in a game. Each person...Ch. 7 - Each of m+2 players pays 1 unit to a kitty in...Ch. 7 - The number of goals that J scores in soccer games...Ch. 7 - Prob. 7.65PCh. 7 - Prob. 7.66PCh. 7 - Prob. 7.67PCh. 7 - Prob. 7.68PCh. 7 - Type i light bulbs function for a random amount of...Ch. 7 - The number of winter storms in a good year is a...Ch. 7 - In Example 5c, compute the variance of the length...Ch. 7 - Prob. 7.72PCh. 7 - The number of accidents that a person has in a...Ch. 7 - Repeat Problem 7.73 when the proportion of the...Ch. 7 - Consider an urn containing a large number of...Ch. 7 - In problem ,suppose that the coin is tossed n...Ch. 7 - Suppose that in Problem 7.75, we continue to flip...Ch. 7 - In Example 6b, let S denote the signal sent and R...Ch. 7 - In Example 6c y)2].Ch. 7 - The moment generating function of X is given by...Ch. 7 - Let X be the value of the first die and Y the sum...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - Prob. 7.83PCh. 7 - Successive weekly sales, in units of $1,000, have...Ch. 7 - Show that E[(Xa)2] is minimized at a=E[X].Ch. 7 - Suppose that X is a continuous random variable...Ch. 7 - Prob. 7.3TECh. 7 - Let X be a random variable having finite...Ch. 7 - Prob. 7.5TECh. 7 - Prob. 7.6TECh. 7 - Prob. 7.7TECh. 7 - We say that X is stochastically larger than Y,...Ch. 7 - Prob. 7.9TECh. 7 - A coin having probability p of landing on heads is...Ch. 7 - Let X1,X2,....Xn be independent and identically...Ch. 7 - Prob. 7.12TECh. 7 - Let X1,X2,... be a sequence of independent random...Ch. 7 - Prob. 7.14TECh. 7 - Prob. 7.15TECh. 7 - Prob. 7.16TECh. 7 - Prob. 7.17TECh. 7 - Prob. 7.18TECh. 7 - In Example 41 t, we showed that the covariance of...Ch. 7 - Show that X and Y are identically distributed and...Ch. 7 - Prob. 7.21TECh. 7 - Prob. 7.22TECh. 7 - Prob. 7.23TECh. 7 - Show that Z is a standard normal random variable...Ch. 7 - Prove the Cauchy-Schwarz inequality, namely,...Ch. 7 - Show that if X and Y are independent, then...Ch. 7 - Prove that E[g(X)YX]=g(X)E[YX].Ch. 7 - Prove that if E[YX=x]=E[Y] for all x, then X and Y...Ch. 7 - Prob. 7.29TECh. 7 - Let X1,...,Xn be independent and identically...Ch. 7 - Consider Example 4f, which is concerned with the...Ch. 7 - An urn initially contains b black and w white...Ch. 7 - For an event A, let IA equal 1 if A occurs and let...Ch. 7 - A coin that lands on heads with probability p is...Ch. 7 - For another approach to Theoretical Exercise 7.34,...Ch. 7 - The probability generating function of the...Ch. 7 - One ball at a time is randomly selected from an...Ch. 7 - Prob. 7.38TECh. 7 - Prob. 7.39TECh. 7 - The best quadratic predictor of Y with respect to...Ch. 7 - Use the conditional variance formula to determine...Ch. 7 - Let X be a normal random variable with parameters...Ch. 7 - It follows from Proposition 6.1 and the fact that...Ch. 7 - Show that for random variables X and Z,...Ch. 7 - Prob. 7.45TECh. 7 - Verify the formula for the moment generating...Ch. 7 - For a standard normal random variable Z, let...Ch. 7 - Prob. 7.48TECh. 7 - Prob. 7.49TECh. 7 - The positive random variable X is said to be a...Ch. 7 - Let X have moment generating function M(t), and...Ch. 7 - Use Table 7.2 to determine the distribution of...Ch. 7 - Show how to compute cov(X,Y) from the joint moment...Ch. 7 - Suppose that X1,...,Xn have a multivariate normal...Ch. 7 - If Z is a standard normal random variable, what is...Ch. 7 - Suppose that Y is a normal random variable with...Ch. 7 - Consider a list of m names, where the same name...Ch. 7 - Prob. 7.2STPECh. 7 - Prob. 7.3STPECh. 7 - Prob. 7.4STPECh. 7 - Prob. 7.5STPECh. 7 - Prob. 7.6STPECh. 7 - Prob. 7.7STPECh. 7 - Prob. 7.8STPECh. 7 - Prob. 7.9STPECh. 7 - Prob. 7.10STPECh. 7 - Prob. 7.11STPECh. 7 - Prob. 7.12STPECh. 7 - Prob. 7.13STPECh. 7 - Prob. 7.14STPECh. 7 - Prob. 7.15STPECh. 7 - Prob. 7.16STPECh. 7 - Prob. 7.17STPECh. 7 - Prob. 7.18STPECh. 7 - There are n items in a box labeled H and m in a...Ch. 7 - Let X be a nonnegative random variable having...Ch. 7 - Let a1,...,an, not all equal to 0, be such that...Ch. 7 - Prob. 7.22STPECh. 7 - Prob. 7.23STPECh. 7 - Prob. 7.24STPECh. 7 - Prob. 7.25STPECh. 7 - Prob. 7.26STPECh. 7 - Prob. 7.27STPECh. 7 - Prob. 7.28STPECh. 7 - Prob. 7.29STPECh. 7 - Prob. 7.30STPECh. 7 - Prob. 7.31STPECh. 7 - Prob. 7.32STPECh. 7 - Prob. 7.33STPE
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
- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2arrow_forwardCustomer Preference Two movie theatres that show several different movies each night compete for the same audience. Of the people who attend theatre A one night, 10 will attend again the next night and 5 will attend Theatre B the next night. Of the people who attend Theatre B one night, 8 will attend again the next night and 6 will attend Theatre A the next night. Of the people who attend neither theatre one night, 3 will attend Theatre A the next night and 4 will attend Theatre B the next night. Find and interpret the steady state matrix for this situation.arrow_forwardAn undergraduate psychology course only gives the grades of A, B, C, or F. The department has determined that there should be 20% A's given, 30% B's given, 40% C's, and 10% F's given as final grades for the course. For the spring 2021 semester, 400 students took the course and 100 students received A's, 100 students received B's, 150 students received C's and 50 students received F's, so taose are my obsérved frequencies. We want to do a Chi-square Multinomial Goodness of Fit test to see if our grading guidelines match up with what is actually happening. What is the expected frequency for the grade of C category? Round your answer to the tenths position.arrow_forward
- a company manufactures a total of 8000 motorcycles a month in three plants A, B and C Of the 8000 motorcycles , plant A manufactures 4000, and plant B manufacturers 3000. At plant A, 85 out of 100 motorcycles are of standard quality or better. At plant B, 65 out of 100 motorcycles are of standard quality or better. At plant B, 65 out of 100 motorcycles are of standard quality or better and at plant C, 60 out of 100 motorcycles are of standard quality or better.The quality controller randomly selects a motorcycle: a) Caculate the probability that its qualtiy is sub-standard, b) If the motorcycle is of sub-standard quality calculate the probability that it has come from plant B.arrow_forwardThe dependencies between the 10 activities listed in the table above are as follows:• The project starts with two activities—A, and B—which can be done concurrently.• When activity A is finished, activity C can start• When activity B is finished, activities D and E can start• When both activities C and D are finished, activity F can start• When activity E is finished, activity G can start• When activity F is finished, activity H can start• When both activities G and H are finished, activity I can start• When activity G is finished, activity J can start• The project is complete when activities I and J are finished Questions1. Organize the information above in an activity precedence table showing the activity, precedent and duration (calculated using the PERT weighted average formula and round to the nearest integer).2. Draw an AON network diagram and calculate its early start, early finish, late start and late finish times, floats (Free and total) for each activity. Make sure you…arrow_forwardA computer store sells three types of microcomputers, brand A, brand B, and brand C. Of the computers they sell, 65% are brand A, 30% are brand B, and 5% are brand C. They have found that 15% of the brand A computers, 10% of the brand B computers, and 5% of brand C computers are returned for service during the warranty period. If a computer is returned for service during the warranty period, what is the probability that it is a brand A computer? A brand B computer? A brand C computer?Question content area bottomPart 1The probability that it is a brand A computer is enter your response here.(Type a decimal. Round to three decimal places if needed.)Part 2The probability that it is a brand B computer is enter your response here. (Type a decimal. Round to three decimal places if needed.)Part 3The probability that it is a brand C computer is enter your response here.(Type a decimal. Round to three decimal places if needed.)arrow_forward
- Human blood may contain either or both of two antigens, A and B. Blood that contains only the A antigen is called type A, blood that contains only the B antigen is called type B, blood that contains both antigens is called type AB, and blood that contains neither antigen is called type O. At a certain blood bank, 35% of the blood donors have type A blood, 10% have type B, and 5% have type AB. (i) What is the probability that a randomly chosen blood donor is type O? (ii) A recipient with type A blood may safely receive blood from a donor whose blood does not contain the B antigen. What is the probability that a randomly chosen blood donor may donate to a recipient with type A blood? (b) A box contains 10 fuses. Eight of them are rated at 10 amperes (A) and the other two are rated at 15 A. Two fuses are selected at random. (i) What is the probability that the first fuse is rated at 15 A? (ii) What is the probability that the second fuse israted at 15 A, given that the first fuse is rated…arrow_forwardWe have three different drugs T, F and H. Drugs T and F cure a V virus in 60% and 80% of cases, respectively, and drug H is entered by mistake in the prescription and if it is administered to patients with the V virus produces serious secondary effects in them without curing the virus. Assume that the effects of the 3 drugs are independent. The treatment consists: first, one of the drugs is randomly administered. After a defined time, if it is not cured, one of the remaining drugs is randomly administered; if it is not cured either, then the third of the drugs is administered. In addition, in the face of serious side effects caused by H, the treatment is interrupted, that is, no other prescription is administered. What is the probability that the patient will be cured of the V virus?arrow_forwardA computer store sells three types of microcomputers, brand A, brand B, and brand C. Of the computers they sell, 65% are brand A, 25% are brand B, and 10% are brand C. They have found that 15% of the brand A computers, 15% of the brand B computers, and 5% of brand C computers are returned for service during the warranty period. If a computer is returned for service during the warranty period, what is the probability that it is a brand A computer? A brand B computer? A brand C computer? .... . The probability that it is a brand A computer is. (Type a decimal. Round to three decimal places if needed.)arrow_forward
- A computer store sells three types of microcomputers, brand A, brand B, and brand C. Of the computers they sell, 60% are brand A, 25% are brand B, and 15% are brand C. They have found that 20% of the brand A computers, 15% of the brand B computers, and 10% of brand C computers are returned for service during the warranty period. If a computer is returned for service during the warranty period, what is the probability that it is a brand A computer? A brand B computer? A brand C computer? The probability that it is a brand A computer is (Type a decimal. Round to three decimal places if needed.) The probability that it is a brand B computer is (Type a decimal. Round to three decimal places if needed.) The probability that it is a brand C computer is (Type a decimal. Round to three decimal places if needed.)arrow_forwardDigi-Key is a large distributor (but not manufacturer) of electronic components. They receive shipments of components from manufacturers and sell them on to other manufacturers, consumers, and hobbyists. An electrical fuse is generally a small device meant to protect other electrical components from damaging surges of electrical current. Suppose Digi-Key receives shipments of a particular fuse in boxes of 20,000 fuses. The manufacturer of this fuse claims that just 1 out of every 100 fuses is defective. Digi-Key draws 50 fuses randomly from each box and tests them using an error-free method. If it finds 2 or more defective fuses in its sample of 50 fuses, it sends that box back to the manufacturer and gets a replacement box. (Because there are 20,000 fuses in a box--much bigger than 50--you may treat this as if it is sampling with replacement even though it is not really.) Compute the probability that Digi-Key sends a box back to the manufacturer if the manufacturer's claim (that…arrow_forwardconditions 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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License