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- Suppose a data set from a bike share company contains the number of daily bike rentals at each of 6 stations for the 23 weekdays of a particular month, i.e. we have Yij for i = 1, ..., 23 and j 1,...6. Write down a hierarchical normal model that can be used to estimate the mean number of bike rentals at each station. You can assume that the unknown variance o? of the number of bike rentals is the same for each station.Two computer companies are offering new software to universities. Let X and Y denote the number of software installed in three major universities by these two companies. Suppose that the variance of X is 539, the variance of Yis 754, and the covariance of X and Yis 183.50. a) Calculate the correlation coefficient (p) Select one: a. 0.287 b. 0.857 c. None of the answers d. 0.9281) Suppose the following model y; = B1 + u; Where is assumed to be normally distributed with mean zero and variance ơ² . Calculate analytically, following OLS technique, ß, and Var(ß,).
- There are two random variables X and Y, and their correlation coefficient pX,Y = 0.7. Now, we have two new random variables A = 2.5X+1 and B = 4Y+2. Please compute the correlation coefficient of A and B, PA,B Please round your answer to one decimal place.A manufacturing company is interested in buying one of two different kinds of machines for production purposes. The first machine was run for 20 hours. It produces on average of 40 items per hour with variance of 8 items2. The second machine was run for 15 hours. It produces on average 50 items per hour with variance of 10 items2. Assume that the production per hour for each machine is (approximately) normally distributed and there a homogeneity between the populations' variances of the number of items produced by the 2 machines Compute 90% confidence interval for the difference between the two means. What is the tabulated value What is the S.E value What Is the lower and upper boundA survey of the white and nonwhite population in a local area reveals the following annual trip frequencies to the nearest state park: X̄1 = 4.1 X̄2= 3.1 s21 = 14.3 s22= 12.0 N1= 20 N2= 16 Where the subscript '1' denotes the white population and the dubscript '2' denotes the nonwhite population. (a) assume the variances are equal, and test the null hypothesis that there is no difference between the park-going frequences of whites and nonwhites (d) Associated with the test in part (a), find a 95% confidence interval for the difference in means
- 5. A quality control engineer found that the inner and outer diameters of their ball bearings, denoted respectively as X and Y, are random variables with E(X|Y = y) = 0.7 – 0.3y inches and Var(X|Y = y) = 0.0004y for all values of y. From his past experience he also knew that the mean and variance of the outer diameters were E(Y) = 0.7 inches, and Var(Y) squared inches. = 0.0001 %3D • (i) What are the conditional random variables, E(X|Y) and Var(X|Y)? • (ii) Find the mean of the inner diameters, E(X). • (ii) Find the variance of the inner diameters, Var(X).just please answer the sub-bLet S1^2 be the sampling variance for a random sample of twelve values (amount of mercury in the blood) and let S2^2 be the sampling variance for a random sample of ten values (amount of lead in the blood); samples from the same population were used. The population variance for mercury measurements is assumed to be twice the corresponding population variance for lead measurements. We will further assume that S1^2 is independent of S2^2. 1. Find a number b such that P [(S1^2/S2^2)<=b]=0.95 enter such a b to three decimal places b= 2. Consider the number b calculated above, find a number a such that P[a<=(S1^2/S2^2)<=b]=0.90 enter said a to three decimal places. a=
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