Assume that the samplefollows the linear model (9.6.1). Suppose Y0 is a future observation at  and we want to determine a predictive interval for it. Assume that the model (9.6.1) holds for Y0; i.e.,  has adistribution. We use ˆ_0 of Exercise 9.6.6 as our prediction of Y0. (a) Obtain the distribution of , showing that its variance is: View complete question » Assume that the […]

Let  be an observation from one of two bivariate normal distributions, I and II, each with  but with the respective variance covariance matrices

1. Show that the square of a noncentral T random variable is a noncentral F random variable 2. Let X1 and X2 be two independent random variables. Let X1 and Y =

Let  be a random sample from a Poisson distribution with parameter _ 0. (b) Express the MVUE as a function of the mle of _. (c) Determine the asymptotic distribution of the mle of _. (d) Obtain the mle of P(X _ 1). Then use Theorem 5.2.9 to determine its asymptotic distribution. Theorem 5.2.9

1. Under Model (9.2.1), show that the linear functions  are uncorrelated. 2. The following are observations associated with independent random samples from three normal distributions having equal variances and respective means Using R or another statistical package, compute the F-statistic that is used to test

The pdf depicted in Figure 7.9.1 is given by where  (the pdf graphed is for m2 = 0.1). This is a member of a large family of pdfs, log F-family, which are useful in survival (lifetime) analysis; see Chapter 3 of Hettmansperger and McKean (2011). (a) Let W be a random variable with pdf (7.9.2). Show that W = log Y , where Y has […]

1. Let  denote a random sample from a distribution that is  Find the MVUE of _2. 2. Let denote a random sample from a distribution that is N(0, _). Thenis a complete sufficient statistic for _. Find the MVUE of

The following data are observations of the random variable , where W has a Bernoulli distribution with probability of success 0.70; Y1 has a N(100, 202) distribution; Y2 has a N(120, 252) distribution; W and Y1 are independent; and W and Y2 are independent. Data are in the file mix668.rda. Program the EM algorithm for this mixing problem as discussed at the end of the […]

1. Describe the limitations of file-processing systems. How do database systems make it possible to overcome these limitations? 2. Using the Internet, trace the history of ANSI and ISO and their relevance to the information systems discipline. Write a summary of your findings.

Let  and  be independent random samples from the distributions (a) Show that the likelihood ratio for testing against all alternatives is given by

Let  be a random sample of size n = 5 from the normal distribution N(0, _). (b) Does 5R/2 have an F-distribution with 2 and 5 degrees of freedom? Explain your answer. (c) Compute E(R) using Exercise 7.9.4. Exercise 7.9.4 Let X and Y be random variables such thatexist for k = 1, 2, 3,… . If the ratio X/Y and its denominator Y are […]

(Telephone Data). Consider the data presented below. The responses (y) for this data set are the numbers of telephone calls (tens of millions) made in Belgium for the years 1950 through 1973. Time, the years, serves as the predictor variable (x). The data are discussed on page 172 of Hettmansperger and McKean (2011) and are in the file telephone.rda.   (a) Calculate the least squares […]

Let _1, _2, _3 be, respectively, the means of three normal distributions with a common but unknown variance _2. In order to test, at the _ = 5% significance level, the hypothesis H0 : _1 = _2 = _3 against all possible alternative hypotheses, we take an independent random sample of size 4 from each of these distributions. Determine whether we accept or reject H0 […]

1. What is the role of normalization in the database design process? 2. Figure 8.1 illustrates how a first normal form violation of ALBUM can be resolved. Suppose that a single album could never have more than four artists. Describe another approach for defining ALBUM that does not violate first normal form. Figure 8.1

Using the results of Example 6.2.4, find an exact size _ test for the hypotheses (6.3.21). Example 6.2.4

Let  be a random sample from a Poisson distribution with mean _ 0. Consider testing (a) Obtain the Wald type test of expression (6.3.13). (b) Write an R function to compute this test statistic. (c) For _0 = 23, compute the test statistic and determine the p-value for the following data.

On page 123 of their text, Kloke and McKean (2014) present the results of an experiment investigating 4 drugs (treatments) for their effect on lowering LDL (low density lipids) cholesterol. For the experimental design, 39 quail were randomly assigned to one of the 4 drugs. The drug was mixed in their food, but, other than this, the quail were all treated in the same way. […]

We consider a random sample  from a distribution with pdf (a) Record the joint pdf of these order statistics and denote it by L(_). (b) Under these conditions, find the mle,  by maximizing L(_). (c) Find the mgf and pdf of (d) With a slight extension of the definition of sufficiency, is  a sufficient statistic?

1. Show that the inverse of the cdf given in expression (10.9.17) is correct. 2. Let IF(x) be the influence function of the sample median given by (10.9.20). Determine E[IF(X)] and Var[IF(X)]. 3. Let be a realization of a random sample. Consider the Hodges–Lehmann estimate of location given in expression (10.9.4). Show that the breakdown point of this estimate is 0.29. corrupted Walsh averages. Hence […]

Consider the situation described in Example 6.6.1. But suppose we have left censoring. That is, if  are the censored items, then all we know is that each . Obtain the EM algorithm estimate of _. Example 6.6.1

Two generators are supplying load as shown in Figure 12.45, where H is the machine inertia, TG is the turbine time constant, Pm is the generator mechanical power, L is the frequency-dependent load, and R is the frequency regulation constant (droop). Initially, L = 1.8 pu, which is supplied by Pm10 = Pm20 = 0.9 pu. (a) If _L = 0.1 pu is inserted, find […]

Use the variational method to estimate the ground state energy of the spherical harmonic oscillator by means of the following radial trial functions: is a normalization constant that needs to be found in each case and : is an adjustable parameter.

Repeat the induction motor startup problem in Example 11.7 by changing the reactance between Buses 2 and 3 from 0.02 pu to 0.08 pu. Keep the induction motor rating at 15 MVA. How long does it take for the Bus 4 voltage to reach 1 pu? Example 11.7

Ignoring the spin of the electron, calculate to first-order perturbation theory the energy of the  level of a hydrogen atom when subject to a weak quadrupole fieldwhere Q is a small, real number

A friend gives you two U.S. coins that equal 55 cents. One of them is not a nickel.What is the other coin? 1. How many species did Moses take on the ark? 2. Some months have 30 days, some 31. How many have 28? 3. How much dirt is contained in a hole 2 ft by 2 ft by 1 ft? 4. A farmer had […]

Does a plaintiff with a case involving a federal question have a choice between state and federal courts? What jurisdictional factors influence his decision about where to file his action? 1. Why does the notice of removal in Exhibit 5–1 state that the noticing defendants are the only ones that have been served?

How is the “hold” at the beginning of the litigation different from that for discovery? Why? How is the summary judgment “hold” for state court cases different from that for federal court cases? 1. Why does an order granting summary judgment not specify which issues are without substantial controversy? 2. Why does the motion for summary judgment and summary adjudication in the exhibits for this […]

Calculate the ground state energy of the doubly ionized beryllium atom  by means of the following two methods and then compare the two results: (a) a first-order perturbation theory treatment, (b) the variational method with a trial functionwhere A is the normalization constant, : is an adjusted parameter, and a is the Bohr radius.

If you represented two California plaintiffs who each had claims of $24,000 plus $2,300 interest against a Nevada corporation, could you bring the action in a California federal court? Why or why not? Would your answer be different if the federal court were located in Nevada? 1. How are two unrelated claims pursued in the same action? How would you decide whether to pursue more […]

Use the variational method to estimate the ground state energy of a particle of mass m that is moving in a one-dimensional potential is the normalization constant and : is an adjustable parameter that needs to be determined.