1d'ydi²Give the general solution ofdy+3+2y=0dtThen find values of a and ß so that the solution of the following differenceequation can be the same at every sample timey((k+2)7) + ay((k+1)7) + By(k)=0To complete this match, we have to find the initial conditions for the secondequation that correspond to the initial conditions of the original differentialequation.(1) If y(0)= y, and dy(0)/dt = y, find initial conditions y(kT) and y((k+1)T) for k=0so that the solutions really are identical at every sample time kT.(2) Note, sometimes we use y(-7) instead of y(+7) for the second initial condition.Find these initial conditions of this type for the difference equation so the solutionsare identical at the sample times.

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Answered: d'y + 3 dy +3+2y=0 di² dt Then find…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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Population Genetics-First Cousins This is a continuation of Exercise 5. Double first cousins are first cousins in two waysthat is, each of the parents of one is a sibling of a parent of the other. First cousins in general have six different grandparents whereas double first cousins have only four different grandparents. For mating between double first cousins, the proportions of the genotypes of the children can be accounted for in terms of those of parents, grandparents, and great-grandparent: 3=122+14+18. a. Find all solutions to the cubic equation above and Identify which is 1. b. After 5 generations, what proportion of the population will be homozygous? c. After 20 generations, what proportion of the population will be homozygous? 5. Population 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?
Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and Ha : p > 0.97).The test results in a P-value of 0.012. In reality, the machine is producing 97% good parts.What probably happens as a result of our testing? A. We correctly reject H0. B. We fail to reject H0, making a Type II error. C. We reject H0, making a Type I error. D. We fail to reject H0, making a Type I error. E. We correctly fail to reject H0.
Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and Ha : p > 0.97). The test results in a P-value of 0.012. In reality, the machine is producing 97% good parts. What probably happens as a result of our testing? We fail to reject H0, making a Type II error. We reject H0, making a Type I error. We correctly reject H0. We fail to reject H0, making a Type I error. We correctly fail to reject H0.
4) Using Gauss-Seidel Method, determine Y4if initial guess X1= 5, Y1= 4, Z1 = 3 6) Using Gauss-Seidel Method, determine Z4if initial guess X1= 5, Y1= 4, Z1 = 3.
Suppose X-Geometric(p=3/4) and Y- Poisson(3) . Find P(X<=2). Find P(Y<4 | Y>=3) . Assume the variables are independent. Find i. E(X+3Y-2) and ii. Var(X+3Y-2) .
The problem is "Twelve percent of the job applicants for a large company have recently smoked marijuana. The company gives all applicants a drug test. The test is not perfect. The test has a sensitivity of 98%- meaning that 98% of those who have recently smoked marijuana will test positive, the other 2% will test negative. The test has a specificity of 96%- meaning that if someone has not recently smoked marijuana, the test will correctly yield a negative test result 96% of the time." M = applicant has recently smoke marijuanaC= applicant has not recently smoked marijuana (clean)X = positive test (test indicates that the person has not recently smoked marijuana recently)N= negative test (test indicates that the person has not recently smoke marijuana) a. What proportion of those who test positive have not recently smoked marijuana? b. What proportion of those who pass the drug test really shouldn’t have?
The problem is "Twelve percent of the job applicants for a large company have recently smoked marijuana. The company gives all applicants a drug test. The test is not perfect. The test has a sensitivity of 98%- meaning that 98% of those who have recently smoked marijuana will test positive, the other 2% will test negative. The test has a specificity of 96%- meaning that if someone has not recently smoked marijuana, the test will correctly yield a negative test result 96% of the time." M = applicant has recently smoke marijuana C= applicant has not recently smoked marijuana (clean) X = positive test (test indicates that the person has not recently smoked marijuana recently) N= negative test (test indicates that the person has not recently smoke marijuana) a. draw a tree diagram for this case b. What proportion of the applicants get an incorrect test result? c. What proportion of the applicants test positive?
Two samples from the same population both have M = 84 and s2 = 20, however one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare [Explain your answer]? The larger sample is more likely to reject the hypothesis and will produce a larger value for Cohen’s d. The larger sample is more likely to reject the hypothesis but the two samples will have the same value for Cohen’s d. The larger sample is less likely to reject the hypothesis and will produce a larger value for Cohen’s d. The larger sample is less likely to reject the hypothesis but the two samples will have the same value for Cohen’s d.
If you found t(60) = 1.70, one tailed, what can we conclude about this results significance? A) The t obtained value exceeds the critical value at the p < 0.05 level but not the p < 0.01 level B) The t obtained value exceeds the critical value at the p < 0.05 level and the p < 0.01 level C) The t obtained value does not exceed either the critical value at the p < 0.05 level or the p < 0.01 level D) The t obtained value exceeds the critical value at the p < 0.01 level but not the p < 0.05 level

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d'y + 3 dy +3+2y=0 di² dt Then find values of a and 3 so that the solution of the following difference equation can be the same at every sample time y((k+2)7)+ay((k+1) 7) + By(k)=0 To complete this match, we have to find the initial conditions for the second