A blockchain-based business received consensus validation via two different systems A and B. The timebetween validations for each validation system in a typical day is known to be exponentially distributed with amean of 3.2 seconds. Both systems operate independently.Given the above distribution, the probability that no validation will be received from system A in a 5-secondperiod is(expressed your answer in 4 decimal places).Likewise, the probability that no validation will be received from both systems in a 5-second period is(expressed your answer in 4 decimal places).If X denotes the number of validations in a 5-second interval. Then, X is a Poisson random variable with thelambda is equal to(expressed your answer in 4 decimal places).Then, the probability that both systems receive two validations between 10 and 15 seconds after the site is(expressed in 4 decimal places).officially open for business is

Answered: validation system in a ty mean of 3.2…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A restaurant has 5 lines. Customers being dispatched to each line at a .25 probability. If customers arrive at the restaurant using an exponential distribution of 10 seconds on average, what's the minimum service rate needed at each line?
Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure. Assume that a plant has two gauges to measure the level of coolant in the reactor core and that each gauge has probability 0.01 of failing. Assume that one potential cause of gauge failure is that the electric cables leading from the core to the control room where the gauges are located may burn up in a fire. Someone wishes to estimate the probability that both gauges fail, and makes the following calculation: P(both gauges fail) = P(first gauge fails) × P(second gauge fails) = (0.01)(0.01) = 0.0001 What assumption is being made in this calculation? Explain why this assumption is probably not justified in the present case. Is the probability of 0.0001 likely to be too high or too low? Explain.
Many diagnostic tests for detecting diseases do not test for the disease directly but for a chemical or biological product of the disease, hence are not perfectly reliable. The sensitivity of a test is the probability that the test will be positive when administered to a person who has the disease. The higher the sensitivity, the greater the detection rate and the lower the false negative rate. Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 85%. A person who actually has the disease is tested for it using this procedure by two independent laboratories. The probability that both test results will be positive is Blank 1 The probability that at least one of the two test results will be positive Blank 2 (round off your answer to four decimal places)
A psychologist studied the effect of defendants' likeability and nervousness on willingness to convict the defendant. Each participant read a transcrip a trial and watched a brief videotape that supposedly showed the defendant on the witness stand. The actor who played the defendant varied the for possibilities of likeable versus not and nervous versus not. After viewing the tape, participants rated the likelihood that the defendant is innocent (1 = unlikely, 10 = very likely). The data are given in the accompanying data table. Complete parts (a) through (d) below. Click the icon to view the data table. Click here to view page 1 of the table of cutoff values for the F distribution. Click here to view page 2 of the table of cutoff values for the F distribution. Click here to view page 3 of the table of cutoff values for the F distribution. Click here to view page 4 of the table of cutoff values for the F distribution (a) Carry out the analysis of variance (use the 0.05 significance…
The effect of cloud seeding on suppression of damaging hail is being studied in your area by randomly seeding or not seeding equal numbers of candidate storms. Suppose the probability of damaging hail from a seeded storm is 0.10, and the probability of damaging hail from an unseeded storm is 0.40. If one of the candidate storms has just produced damaging hail, what is the probability that it was seeded
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You are the manager of a manufacturing plant and you are responsible for quality control. Each day, a random sample of 10 items is selected from the production line and tested by a quality control technician. A item can be in good condition or defective, and the probability that an item is defective is 0.05. You know by experience that the technician records the result of the test on an item correctly 80% of the time. Let X be the number of items that were recorded as defective by the technician (in the sample of 10 tested items). (a) Find the probability P(X= 1). (b) If the technician recorded one defective item in the sample, what is the conditional probability that there was no defective item in the sample?
The number of accidents at a certain intersection is a Poisson random variable. The probability that there are 2 accidents in any given week is 3 times as much as the probability that there are 4 accidents in any given week. Find the probability that there are no accidents at the intersection next week.
A recent survey in Montana revealed that 20% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of 10 vehicles traveling on US 131 higway. Let X denote the number of vehicles that were exceeding the limit. What is the probability that fewer than 6 vehicles were exceeding the limit?
Trains arrive at a major train-station randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 4 trains per hour. What is the probability that 8 trains will arrive during any given hour of operation?
After an introductory statistics course, 80% of students can successfully construct box plots. Of those who can construct box plots, 86% passed, while only 65% of those students who could not construct box plots passed. Calculate the probability that a student is able to construct a box plot if it is known that he passed. P(Bplot = Success) = 0.8 P(Bplot = Success | Passed = Yes) = 0.86 p(Bplot = Failed | Passed = Yess) = 0.65
At a certain large company, the floor manager reviewing inventory and production. She ultimately comes to the decision that a product should be continued if it sold 150,000 times over the previous year. In addition, the product is considered “popular” if it receives at least 100 mentions by the local press over the past year. An analyst is hired to help with the analysis. The analyst determines that the probability of sales exceeding 150,000 was 0.331, the probability of 100 or more mentions was 0.162, and the probability that a product both sold 150,000 items, and was also ‘popular’ is 0.064. What is the probability that a randomly selected product either sold the requisite 150,000 items, or that it is ‘popular’? Again, phrase your answers in terms of probability variables (e.g. P(X) = ..., P(Y)=... etc.) If we are told that an item has indeed reached the threshold of 100 mentions in the press, what is the probability of it selling 150,000 times? Thought Question: Where would the…

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