7. Chess continued. A rook and a bishop perform independent symmetric random walks with synchronous steps on a 4 x 4 chessboard (16 squares). If they start together at a corner, show that the expected number of steps until they meet again at the same corner is 448/3.
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![7. Chess continued. A rook and a bishop perform independent symmetric random walks with
synchronous steps on a 4 x 4 chessboard (16 squares). If they start together at a corner, show that the
expected number of steps until they meet again at the same corner is 448/3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4ad6836-b6cb-4e61-ab16-9fcd3f7da648%2F637bd703-ed8a-44b1-921f-43a5e953118c%2Fzv2ldo_processed.jpeg&w=3840&q=75)
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- The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 2 employees were assigned to assemble the subassemblies. They produced 11 during a one-hour period. Then 4 employees assembled them. They produced 18 during a one-hour period. The complete set of paired observations follows. Number ofAssemblers One-HourProduction (units) 2 11 4 18 1 5 5 23 3 18 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Click here for the Excel Data File Draw a scatter diagram. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1). Repeat the process for the remainder of the sample (No of Assemblers2,…rch A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting 12 workers at random and timing each worker on each assembly process. Half of the workers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) is recorded, as shown in the table below. Worker Process 1 Process 2 Difference (Process 1 - Process 2) Send data to calculator 1 81 67 Explanation Type of test statistic: O 14 Check 2 80 78 2 3 84 65 19 89 72 17 5 81 78 (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho H₁ :0 (b) Determine the type of test statistic to use. 3 6 35 53 7 50 30 -18 20 8 32 34 LG -2 9 45 48 (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the two critical values at the 0.05…A stock index consists of businesses in both Europe and the United States. Assume that each business comprising the stock index makes a profit or loss independently of the other businesses in the index. Suppose that an American business on the stock index makes a profit 60%60% of the time and a European business makes a profit 80%80% of the time. If there are 840 American businesses and 720 European businesses in the stock index, what is the expected number of businesses in the stock index to make a profit?
- A study was conducted to investigate whether local car mechanics charge women more than men for an alternator repair. The researcher selected randomly one man and one woman from everyone who had used the same mechanic for the same alternator repair. The process was repeated for a total of six selected randomly cars. The repair prices and the differences (Women – Men) are shown in the table. Do the data provide convincing statistical evidence that women pay more than men for the same alternator repair?Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides. Since the dice are all rolled at the same time, let the roll (5, 4, 3, 2, 1) to be equal to (2, 4, 5, 1, 3). Assume for this question that we will only be rolling the dice once. (i) How many ways can you roll all the dice? (ii) To win 50 points you would need all the dice to roll the same number (ex. (1, 1, 1, 1, 1)). How many ways can you win the 50 points? (iii) Suppose you are trying to get your dice to roll only consecutive numbers (ex. (1, 2, 3, 4, 5) or (2, 3, 4, 5, 6)) How many different ways are there to do this? (iv) Suppose instead you are trying to get your dice to roll 4 consecutive numbers (ex. (1, 2, 3, 4, 1) or (2, 3, 4, 5, 3)) How many different ways are there to do this? (make sure to not count any only consecutive numbers) This is a combinatorics math counting problem.In 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?
- A small computer lab has 2 terminals. The number of students working in this lab is recordedat the end of every hour. A computer assistant notices the following pattern:- If there are 0 or 1 students in a lab, then the number of students in 1 hour has a50-50% chance to increase by 1 or remain unchanged. - If there are 2 students in a lab, then the number of students in 1 hour has a 50-50%chance to decrease by 1 or remain unchanged. (a) Write the transition probability matrix for this Markov chain.(b) Suppose there is nobody in the lab at 7 am. What is the probability of nobody workingin the lab at 10 am?A building contractor has a chance to buy an odd lot of 1,000 used bricks at an auction. She is interested in determining the proportion of bricks in the lot that are cracked and therefore unusable for her current project, but she does not have enough time to inspect all 1,000 bricks. Instead, she checks 150 bricks to determine which ones are cracked. What is the population of interest? all building contractors all 1,000 bricks in the lot the rest of the 850 bricks the 150 bricks selected for inspection the rest of the 700 bricks What group constitutes the sample? the 150 bricks selected for inspection all building contractors the rest of the 700 bricks all 1,000 bricks in the lot the rest of the 850 brickS Submit Answer7. A new drug study was conducted by a drug company. In the study, 10 people were chosen at random to take Vitamin X for 3 months and then have their cholesterol levels checked. In addition, 10 different people were randomly chosen to take Vitamin Y for 3 months and then have their cholesterol levels checked. All 20 people had cholesterol levels between 8 and 10 before taking one of the vitamins. The drug company wanted to see which of the 2 vitamins had the greatest impact on lowering people's cholesterol. The following data was collected: Vitamin X 7.27.5 5.2 6.5 7.7 10 6.47.6 7.77.8 Vitamin Y 4.8 4.44.5 5.1 6.5 8.03.1 4.6 5.2 6.1 (a) Draw a box-and-whisker plot for both sets of data on the same number line. (b) Use the double box-and-whisker plots to compare the 2 vitamins and provide a conclusion for the drug company. (e) State the skewness of both distributions and justify your answer.
- Itranscript One male and one female dam rat pup were randomly selected from 8 litters to perform the swim maze. Each pup was placed in the water at one end of the maze and allowed to swim until it escaped at the opposite end. If the pup failed to escape after a certain period of time, it was placed at the beginning of the maze and given another chance. The experiment was repeated until each pup accomplished three successful escapes. The table to the right reports the number of swims required by each pup. Is there sufficient evidence of a difference between the mean number of swims required by male and female pups? Use a=0.01. Comment on the assumptions required for the test to be valid. B. t> Litter 1 2 3 OC. t 10 12 Female 11 [6526675 10Diana tested the effect of number of items on short-term memory in dolphins. She randomly presented visual arrays with 1, 2, 3, 5, 8, 13, 21 items for five minutes. She asked 3 dolphins to remember the items. She then presented a new array with old and new items. The dolphins responded by touching the items with their tails. She hypothesized that Dolphins could remember 3 items accurately, but not more than that. How many pairwise comparisons should she do according to the recommended guideline?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.,…
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