Confidence of feedback information for improving quality. In the semiconductor manufacturing industry, a key to improved quality is having confidence in the feedback generated by production equipment. A study of the confidence level of feedback information was published in Engineering Applications of Artificial Intelligence (Vol. 26, 2013). At any point in time during the production process, a report can be generated. The report is classified as either “OK” or “not OK.” Let A represent the
- a. Express the event B|A in the words of the problem.
- b. Express the event B|Ac in the words of the problem.
- c. Find P (Ac).
- d. Find P (A∩B).
- e. Find P (Ac∩B).
- f. Use the probabilities, parts d and e, to find P (B).
- g. Use Bayes’ Rule to find P (A|B), i.e., the
probability that an “OK” report was generated in one time period (t), given that an “OK” report is generated in the next time period ( t + 1).
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Statistics for Business and Economics (13th Edition)
- What term is used to express the likelihood of an event occurring? Are there restrictions on its values? If so, what are they? If not, explain.arrow_forwardPopulation Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?arrow_forwardWhat is an experiment? Give two examples.arrow_forward
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