(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

Help please. I am extremely confused and do not understand this! Can I get help with all parts please
In a classic study of problem solving, Duncker (1945) asked participants to mount a candle on a wall in an upright position so that it would burn normally. One group was given a candle, a book of matches, and a box of tacks. A second group was given the same items, except that the tacks and the box were presented separately as two distinct items. The solution to this problem involves using the tacks to mount the box on the wall, creating a shelf for the candle. Duncker reasoned that the first group of participants would have trouble seeing a new function for the box (a shelf) because it was already serving a function (holding tacks). For each participant, the amount of time to solve the problem was recorded. Data similar to Duncker’s are as follows. Time to Solve Problem (in sec.) Box of Tacks Tacks and Box Separate 128 42 160…
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…
This is a practice exam. I would like to know how to slove usign excel or megastat Wenton Powersports produces dune buggies. They have three assembly lines, “Razor,” “Blazer,” and “Tracer,” named after the particular dune buggy models produced on those lines. Each assembly line was originally designed using the same target production rate. However, over the years, various changes have been made to the lines. Accordingly, management wishes to determine whether the assembly lines are still operating at the same average hourly production rate. Production data (in dune buggies/hour) for the last eight hours are as follows. (You may find it useful to reference the F table.) Razor Blazer Tracer 11 10 9 10 8 9 8 11 10 10 9 9 9 11 8 9 10 7 12 11 8 12 8 9 Click here for the Excel Data File a. Specify the competing hypotheses to…
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?
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.,…
2. Mobile phone operator TELE2 has at least 4 tariffs: Brivais(B), Savejis(S), Smart(SM), Zelts(Z). In 2019Y the proportion of clients for each tariff is: B=5%; S=50%; SM-15%; Z=30%. Possible changes from one type of tariff to another for the following year are the following: to B to S to SM to Z from B 5% 2% 1% 1% 1% from S 3% 1% from SM 5% 5% from Z 5% 4% 3% Find initial distribution, Transition matrix (stochastic matrix), stationary distribution and plot a graph for transition of one step. bain ic the following
A car rental agency in a major city has a total of 4600 cars that it rents from three locations: Metropolis Airport, downtown, and the smaller City Airport. Some weekly rental and return patterns are shown in the table (note that Airport means Metropolis Airport). Returned to AP DT CA 90% 10% 10% Airport (AP) Downtown (DT) 5% 80% 5% Rented from At the beginning of a week, how many cars should be at each location so that the same number of cars will be there at the end of the week (and hence at the start of the next week)? AP DT CA Need Help? cars cars cars Read It Watch t Talk to a Tutor
V7
A researcher is interested in the effects of cocaine on learning. A group of rats is randomly assigned to receive either cocaine or a non-harmful saline solution. The rats are taught how to run a maze. The cocaine rats need to be reared away from the control group rats, so they are handled and taught by one experimenter, and the control group rats are handled and taught by another experimenter. The results showed that the control group rats learned how to run the maze more quickly than the cocaine rats. 1. What is the independent variable? 2. What is the dependent variable? 3. What is the confounding? 4. How could the confounding be fixed?
As you read about each study, (a) classify the type of research that it reflects, and (b) identify the kinds of conclusions that might reasonably be drawn from the results. An educational psychologist videotapes 20 high school history teachers in action for a period of 4 weeks. He then codes every teacher statement as belonging to one of three categories: whether it (a) presents new information, (b) asks a question, or (c) gives instructions. He summarizes this information and compares the amount of teacher questioning to the students' scores on a district-wide history achievement test given later in the year. The researcher finds that when teachers ask a lot of questions in class, students are more likely to score at high levels on the achievement test. (a) Classify the research as one of the following: Quantitative/descriptive Quantitative/correlational Quantitative/experimental Quantitative/quasi-experimental Qualitative Mixed methods, and…
A market researcher wants to determine whether a new model of a personal computer that had been advertised on a late-night talk show had achieved more brand-name recognition among people who watched the show regularly than among people who did not. After conducting a survey, it was found that 12% of all people both watched the show regularly and could correctly identify the product. Also, 13% of all people regularly watched the show and 39% of all people could correctly identify the product. Define a pair of random variables as shown below. Complete parts (a) through (c). X=1 if regularly watch the show Y=1 if product correctly identified a. Find the joint probability function of X and Y X 0 1 (Do not round.) 0 X=0 otherwise Y=0 otherwise 1 CLLL 2 xdex ram