The article "Statistical Method on Nonrandom Clustering with Application to Somatic Mutations in Cancer" [BMC Bioinformatics, 2011,11(1)] developed a statistical method to discover mutations that lead to cancer by identifying nonrandom clusters of amino acidmutations in protein sequences in cells. In this method, N denotes the length of a protein sequence, and n denotes the total number ofmutations in the protein. The position of a mutation is modeled with a discrete uniform distribution between 1 and N. Suppose thatyou are a biomedical engineer working on a protein sequence with two mutations and length N = 1000. Assume that the locations ofthe mutations are independent, and can be the same for two mutations.(a) Determine the probability that the first mutation occurs in the first half of the protein sequence.P =i(b) Determine the probability that both of the mutations occur in the first half of the protein sequence.P =i(c) Determine the probability that at least one of the mutations occurs in the first half of the protein sequence.P =i

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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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One important aspect of medical diagnosis is its reproducibility. Suppose that two different doctors examine 100 patients for dyspnea in a respiratory-disease clinic and that doctor A diagnosed 15 patients as having dyspnea, doctor B diagnosed 10 patients as having dyspnea, and both doctor A and doctor B diagnosed 7 patients as having dyspnea. 10.16 Compute the Kappa statistic and its standard error regarding reproducibility of the diagnosis of dyspnea in this clinic.
Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from 2%. For quality assurance purposes, you decide to randomly select 1,000 of these electronic components before they are shipped to customers. Of the 1,000 components, you find 25 that are defective. Assume that the company produces a very large number of these components on any given day. Set up an appropriate hypothesis to test whether or not the defect rate has increased. Before proceeding to test your hypothesis, check that all assumptions and conditions are satisfied for such a test. Conduct the test using a .05 level of significance (alpha) and state your decision about…
Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from 2%. For quality assurance purposes, you decide to randomly select 1,000 of these electronic components before they are shipped to customers. Of the 1,000 components, you find 25 that are defective. Assume that the company produces a very large number of these components on any given day. Conduct the test using a .05 level of significance (alpha) and state your decision about whether or not you believe that the defect rate has increased. What would be the minimum number of defectives in a random sample of 1,000 would you need to find in order to statistically decide that the defect…
A geneticist working on peas has a single plant monohybrid Y/y (yellow) plant and, from a self of this plant,wants to produce a plant of genotype y/y to use as a tester. How many progeny plants need to be grown to be 95percent sure of obtaining at least one in the sample?
During the pandemic period, it is claimed that the average of transmitting the virus to others in the case of a person who lives in Europe and is a carrier of Covid-19 virus, in case he does not comply with the social isolation rule, and the average of transmitting the virus to others from the same situation living in America is different from each other. In order to test this claim, 13 of the carriers living in Europe, randomly selected, have an average of 29 and a standard deviation of 13. Similarly, the average transmitting the virus was 33 and the standard deviation was 17 for 17 random carriers living in the United States who did not comply with the social isolation rule. Since it is known that the variances of all people living in Europe and America with the disease are heterogeneous, test the claim at the 13% significance level, interpret the decision you made as a result of the test. While testing the hypothesis test, apply the 4 steps and show them separately.
A random group of students was selected from a large student conference to analyze their class in school Is there evidence to reject the hypothesis that the number of students is equally distributed between the four classesat a = 0.05 ?
An organization published an article stating that in any one-year period, approximately 11.5 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, nine of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country. At a pre-conceived α = 0.05, what are your following?Decision: , Reason for the decision: ,Conclusion
A random group of students was selected from a large student conference to analyze their class in school. Is there evidence to reject the hypothesis that the number of students is equally distributed between the four classes , = 0.052
At a toll-booth on-ramp there is a stochastic arrival distribution. Vehicles are counted in 20-second intervals, and vehicle counts are taken in 120 of these time intervals. Based on data collected, no vehicles arrived in 18 of the 120 count intervals. What is the number of the 120 intervals that 3 cars arrived?
People are classified as hypertensive if their systolic bloodpressure (SBP) is higher than a specified level for their agegroup, according to the algorithm in Table 5.1.Assume SBP is normally distributed with mean andstandard deviation given in Table 5.1 for age groups 1−14and 15−44, respectively. Define a family as a group of twopeople in age group 1−14 and two people in age group15−44. A family is classified as hypertensive if at least oneadult and at least one child are hypertensive. 5.17) What proportion of 1- to 14-year-olds are hypertensive? 5.18) What proportion of 15- to 44-year-olds are hyper-tensive?
Suppose that the probability of making a mistake in translation at each translational step is a small number, δ. Show that the probability, p, that a given protein molecule, containing n residues, will be completely error-free is (1 – δ)n.
The number of Muslims continues to grow throughout the world, and they are currently thesecond-largest religious group in the world. Knowing that this group has been the target of falsebeliefs about their religion, a researcher is interested in whether people who have moreinteractions with Muslim people are less likely to believe negative statements about Islam. To dothis, they surveyed a large sample of participants across Western Europe and asked themquestions about how frequently they interact with Muslim people as well as how much theyagreed with negative statements about Islam. What statistical test should be used to determine ifthere if how frequently survey participants interact with Muslim people predicts how likely theyare to agree with a negative statement about Islam? Assume parametric assumptions are met. A. Is this a relationship test or a difference test? Explain your rationale. B.

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