Uncategorized

1. Let  be a random sample from a uniform distribution. Let min  and let  max . Show that ’ converges in probability to the vector ’ . 2. Let  and  be p-dimensional random vectors. Show that if

1. Suppose distribution, show that 2. Let  be a random sample on  that has a  distribution,  (a) Determine the mle of θ. (b) Suppose the following data is a realization (rounded) of a random sample on

Answer the following questions. Each response must be at least 5 sentences long and must cite each source used.1. How did the Crusades alter European perceptions of the East?2. What aspects of medieval life were altered by the Black Death?3. What key events spurred the Renaissance, why would these lead to humanism becoming a dominant

Prove that X, the mean of a random sample of size n from a distribution that is , is, for every known , an efficient estimator of θ. Given formally compute the reciprocal of Compare this with the variance of where is the largest observation of a random sample of size n from this distribution.

Given the pdf show that the Rao–Cram´er lower bound is 2/n, where n is the size of a random sample from this Cauchy distribution. What is the asymptotic distribution ofif  the mle of θ?

Instructions: You must answer 5 of the following 10 . Answer in essay format, except where it is permitted for you to list. You MUST answer question 1, and you select the other 4. 1. Write an essay in which you explain what an Aristotelian science is. What is scientia? What do we think we know

Obtain an R function that plots the power function discussed at the end of Example 6.3.2. Run your function for the case when , and α = 0.05. Example 6.3.2

Show that the test with decision rule (6.3.6) is like that of Example 4.6.1 except that here σ2 is known. Example 4.6.1

For the test described in Exercise 6.3.6, obtain the distribution of the test statistic under general alternatives. If computational facilities are available, sketch this power curve for the case when  Exercise 6.3.6 Let  be a random sample from a  distribution, where  and  is known. Show that the likelihood ratio test of  

Let  be a random sample from a  distribution, where  and  is known. Show that the likelihood ratio test of