Which of the following sets are linearly independent in p3? S, = {(1.21). (1.-1,0). (1, 1,1)} S3 = ((0,0.–1)- (0,1.0). (-20.0)) OA S1, S3 O B. S3 %3D OC.SS2 O D. S, S3 OES,
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- Consider an individual who is risk-loving instead of risk-averse. a. Is U(I) concave or convex?b. Suppose this person is offered an actuarially fair insurance product that guarantees her a certain income, E[I]. Graph the consumer surplus this person receives from buying this insurance as p, the probability of being sick, varies from 0 to 1. You should plot p on the horizontal axis and consumer surplus on the vertical axis.c. Suppose, finally, that this person is offered a subsidy (perhaps from her parents) for buying insurance so that, if she buys insurance, she will be guaranteed an income γ E[I], where γ >1. With the subsidy, insurance is now actuarially unfair in her favor. Graph how her consumer surplus (M) changes as p, the probability of being sick, varies from 0 to 1. [Hint: draw a coordinate plane with p on the x-axis and M on the y-axis.] Based on this graph, under what conditions is she least likely to buy the subsidized insurance?The data below are the temperatures on randomly chosen days during the summer and the number of employee absences at a local company on those days. Test the claim, at the α = 0.05 level of significance, that a linear relation exists between the two variables, Apply classical and p-value approaches. Show step1-step3. Input β1 as "beta1" or "β1". Do NOT input as "b1". Temperature x 72 85 91 94 100 80 90 78 99 number of absences y 3 7 10 10 8 9 4 15 15 Round critical value and test statistic to nearest hundredth. (0.125 would be entered 0.13) Round p-value to nearest ten-thousandth. (0.14275 would be entered 0.1428)Find the mean and standard deviation for each uniform continuous model U(1, 13) U(70, 200) U(3, 92)
- Here are data on the lengths of male and female roaches (in mm). Your job is to find out if there is adifference between male and female roaches.males 15.4 13.9 12.7 9.6 6.6 10.7 9.9 13.3 16.2 9.0 11.4 16.6 12.2females 16.7 16.3 12.8 16.9 15.1 12.8 18.7 18.3 8.6 13.6 15.3 16.2 13.4It's up to you to figure out what the best procedure is, what kind of hypotheses to use, which α to use,what test to use, and so on. Make sure you follow all the appropriate steps. You should probably use Ras you’ll get done much quicker. Remember to very clearly state your results in writing. Never turn injust an R printout.Hint: how do you decide which test to use? What kind of distributions do the data have?Calculate correlation and probable error between physical parameters (temperature and humidity) in all 3 seasons Order Number of family (x) Number of sites(n) Temperature(y) in autumn Humidity(y) in autumn Temperature (y)in winter Humidity (y)in winter Temperature(y) in spring Humidity(y) in spring Lepidoptera 2 1 24.1 35 19 45.33 27 40.1(A) The linearity between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and Y=[6,4,6,8,5,10] is equal to? (B)An outbreak of certain illness was attributed to ice creams produced at a certain factory. Scientists measured the level of the illness causing factor in 10 randomly sampled batches of ice cream. The levels were: 0.583, 0.242, 0.129, 0.691, 0.231, 0.693, 0.619, 0.392, 0.418. What is the estimated interval of population mean at 0.05 level of significance? (C) The population standard deviation for the age of a certain University students is 13 years. If we want to be 90% confident that the sample mean age is within 3 years of the true population mean age of the University students, then how many randomly selected students must be surveyed?
- By inspection, determine why each of the sets is linearly dependent.(a) S = {(1, −2), (2, 3), (−2, 4)}(b) S = {(1, −6, 2), (2, −12, 4)}(c) S = {(0, 0), (1, 0)}For a χ2-curve with 9 degrees of freedom, find χ20.005, and interpret the value in terms of the χ2-curve. df χ20.10 χ20.05 χ20.025 χ20.01 χ20.005 ... ... ... ... ... ... 6 10.645 12.592 14.449 16.812 18.548 7 12.017 14.067 16.013 18.475 20.278 8 13.362 15.507 17.535 20.090 21.955 9 14.684 16.919 19.023 21.666 23.589 Select the correct answer below: 1) χ20.005 with 9 degrees of freedom = 16.919. This means that the area to the right of the χ2-value 16.919, under the χ2-curve, is 0.005. 2) χ20.005 with 9 degrees of freedom = 16.919. This means that the area to the right of the χ2-value 0.005, under the χ2-curve, is 16.919. 3) χ20.005 with 9 degrees of freedom = 23.589. This means that the area to the right of the χ2-value 0.005, under the χ2-curve, is 23.589. 4) χ20.005 with 9 degrees of freedom = 23.589. This means that the area to the right of the χ2-value 23.589, under the χ2-curve, is 0.005. 5) χ20.005 with 9 degrees of…Assume that the differences are normally distributed. Complete parts (a) through (d) below. Observation 1 2 3 4 5 6 7 8 Xi 52.2 46.5 46.0 44.1 47.7 45.3 50.1 55.6 Yi 52.8 46.1 50.5 49.6 47.9 49.2 51.6 54.8 (a) Determine di=Xi−Yi for each pair of data. Observation 1 2 3 4 5 6 7 8 di negative . 6−.6 . 4.4 negative 4.5−4.5 negative 5.5−5.5 negative . 2−.2 negative 3.9−3.9 negative 1.5−1.5 . 8.8 (Type integers or decimals.) (b) Compute d and sd. d=negative 1.875−1.875 (Round to three decimal places as needed.) sd=2.4212.421 (Round to three decimal places as needed.) (c) Test if μd<0 at the α=0.05 level of significance. What are the correct null and alternative hypotheses? A. H0: μd=0 H1: μd<0 Your answer is correct. B. H0: μd<0 H1: μd=0 C. H0: μd>0 H1: μd<0 D. H0: μd<0 H1:…
