(Devore: Section 3.2 #15) Many manufacturers have quality control programs that include inspec- tion of incoming materials for defects. Suppose a computer manufacturer receives circuit boards in batches of five. Two boards are selected from each batch of inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair (1, 2) represents the selection of boards 1 and 2 for inspection. (a) List the ten different possible outcomes. (b) Suppose that boards 1 and 2 are the only defective boards in a batch. Two boards are to be chosen at random. Define X to be the number of defective boards observed among those inspected. Find the probability distribution (pmf) of X. (c) Let F denote the cdf of X. Determine F(0), F(1) and F(2); then obtain F(x) for all other r.

(Devore: Section 3.2 #15) Many manufacturers have quality control programs that include inspec- tion of incoming materials for defects. Suppose a computer manufacturer receives circuit boards in batches of five. Two boards are selected from each batch of inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair (1, 2) represents the selection of boards 1 and 2 for inspection. (a) List the ten different possible outcomes. (b) Suppose that boards 1 and 2 are the only defective boards in a batch. Two boards are to be chosen at random. Define X to be the number of defective boards observed among those inspected. Find the probability distribution (pmf) of X. (c) Let F denote the cdf of X. Determine F(0), F(1) and F(2); then obtain F(x) for all other r.

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...

See similar textbooks

Similar questions

6. The DNR is planning a study to determine whether breakwaters help decrease erosion at a large lake. They divide the shoreline into 100-foot plots, installing some with breakwaters and some without. However, the east and west shorelines of this lake receive very different wave patterns due to the wind. The DNR suspects this will affect the responses to the breakwaters. Because of this, the DNR plans to treat each shoreline as a different group. This study is an example of (A) An uncontrolled experiment (B) A blocked design experiment. (C) A matched pairs experiment. (D) A stratified random sample (E) A randomized observational study
This graph shows data from people from the sub-Saharan area of Africa who have contracted HIV. Outcomes for the patients were recorded as one of 4 mutually possibilities: alive and still in care at the original clinic, alive and still in care after transferring to a new clinic, alive but no longer visiting a clinic, or they’re dead. Keep in mind that this data were collected are from clinical records. Assume that the sample is a random representation of sub-Saharan Africans with HIV. Antiretroviral therapy is used to treat patients. What is the experimental unit? What are the variables (including the types)?
StarHortons Cup, the coffee company, wants to determine how long caffeine lasts throughout the day when individuals have a cup of one of their 3 types of coffee at 9am. They will then measure the levels of caffeine in these individuals’ systems at 10am, 12am, 2pm, 4pm, 6pm and 8pm. They want to have at least 20 observations per group. How many separate/distinct groups of participants are needed if they want to conduct this experiment using a mixed-measures ANOVA? 18 6 20 3
Let's assume that there are 500 people in a population. The researcher has access to all 500 participants, and sends a questionnaire that is accessed by a hyperlink. Of the 500 possible subjects, 485 complete it. Does this mean that the results generated from this study will be highly-accurate? What might cause the study to be unreliable?
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?
Please fill in the blanks. im stuck. last guy who answered this question for me was wrong.
5. In recent years there has been a great deal of research demonstrating gender discrimination in science, technology, engineering and math (STEM) fields. In one experiment, for example, faculty members viewed an application for a laboratory manager position. The applications were identical except that half had a traditionally male name (John) and half had a traditionally female name (Jennifer). In addition, half of the faculty participants were from STEM fields and half were from non-STEM fields. The faculty were asked to rate the competence of the applicants on a 6-point scale, with 1 indicating a lower rating. Group means are presented below, along with an incomplete summary table. After completing the table, write a conclusion about the outcome of the experiment. Source Gender of applicant Male Female Between Treatments Gender of applicant Discipline of rater A x B interaction Within treatments Total SS 320 80 576 Discipline of Faculty Rater STEM M = 4.80 M = 4.02 df MS 20 1.25…
Scenario 3. A researcher creates a new program for college students to reduce feelings of loneliness and enhance students' engagement on campus. This new program helps students to find student groups and clubs that fit their interests. She randomly assigns students to either enroll in this new program (the experimental group) or to not enroll in the program (the control group). She compares students' feelings of engagement between the two groups, and expects that engagement will be higher among the students that are in the program. What is the most appropriate test statistic to use to test the hypothesis in scenario 3? A) z-test B) z-score C) Independent samples t-Test D) Correlation Coefficient E) One-way ANOVA F) Dependent samples t-Test G) Factor Analysis H) Structural Equation Model What is the null hypothesis for scenario 3? A) H0: engagement in the experimental group ≤ engagement in the control group B) H0 : engagement in the experimental group = engagement in the control…
In a survey of statistics students, it is found that 54 use RStudio, 43 use SAS, and 32 use Stata, for data analysis. Moreover, 29 use both RStudio and SAS, 18 use both RStudio and Stata, and 21 use both SAS and Stata, for data analysis. Fifteen of these students use RStudio, SAS, and Stata, while nine of them use tools other than R Studio, SAS, and Stata. a. How many students use RStudio only for data analysis? b. How many students use at least two software for data analysis? c. How many students use SAS or Stata, but not both?
An 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.
A company claims that its brand of dish detergent, A, is more effective than a competitor’s brand, B. Fifty dirty dishes are randomly selected and randomly divided into two groups. In one group, each dirty dish will be placed in a container of hot water with Brand A detergent and in the other group, each dirty dish will be placed in a container of hot water with Brand B detergent. The dishes will sit for two hours, and then the cleanliness of the dishes will be measured using a scale of 1–10 (1 = least clean to 10 = most clean). The difference in mean cleanliness ratings for the two detergents (A – B) will then be calculated. What is the appropriate inference procedure?
1. For her botany class project, Jennifer wonders if there is a connection between the average weight of watermelons a vine produces and the root depth of the vine. Jennifer suspects that vines with deeper roots have a better water supply and produce larger melons. From a large watermelon field, 10 vines are chosen at random. At the end of 8 weeks, the watermelons are removed from each vine and the average weight of the watermelons from each vine is determined. Each plant is carefully dug up and its root depth (or length) is measure. Let x represent the root depth (to the nearest inch) and y be the mean weight of the watermelons on the vine (in pounds). Suppose that x = 17, s, = 6, y = 12, s, = 5.1, and r = = 0.93. a. Find the equation of the least squares regression line (round a and b to the nearest tenth). b. List 2 points that you know will be on the least-squares line you found in part a. c. What percent of variation is accounted for by a linear relationship? d. Using part a.,…