Problem Set fi, Econ 120C
美国经济学代写 (ii)Handwritten answers have to be scanned and saved in pdf (You can use your phone to takea picture and convert the picture into pdf)
Please follow the guidance below to submit all assignments:
(i)Pleasesubmit your answers, which can be either typed or handwritten on ucsd.edu.
(ii)Handwritten answers have to be scanned and saved in pdf (You can use your phone to takea picture and convert the picture into pdf)
(iii)Please submit only one pdf file for each assignment. If you have multiple files, please combine them into one before submission. 美国经济学代写
(iv)Forthe questions that need Stata, please include your log and figures, if Please do not upload your log and figure files directly. Instead, convert them into pdf and include them in the pdf file you plan to submit.
(v)Again,please submit only one pdf file for each Please do not use any other file format. Please do not submit more than one file.
Part A. Multiple Choice 美国经济学代写
- fi.LetYfi, …, Yn be iid with mean µY . Consistency for the sample average Y¯ can be defined as follows, with the exception of
(a)Y¯ is consistent for µY .
(b)Y¯ has the smallest variance of all
(d)theprobability of Y¯ being in the range µY T c becomes arbitrarily close to one as n increases for any constant c > 0.
2. The OLS estimator is a random variable and
(a)is a single number and as a result cannot havea distribution.
(b)has a probability distribution called its sampling distribution.
(c)hasa probability distribution called the standard normal distribution.
(d)has a probability distribution called normal distribution.
3.Toinfer the political tendencies of the students at your college/university, you sample fi†O of them. Only one of the following is a simple random sample:
(a)You make sure that the proportion of minorities are the same in your sample as in the entire student body.
(b)call every fiftieth person in the student directory at 9 a.m. If the person does not answer the phone, you pick the next name listed, and so on.
(c)go to the main dining hall on campus and interview students randomly there.
(d)have your statistical package generate fi†O random numbers in the range from fi tothetotal number of students in your academic institution, and then choose the corre- sponding names in the student telephone directory. 美国经济学代写
- Let Yfi, …, Ynbe iid with mean µY and variance oX . The central limit theorem states that
(a)thedistribution for Y¯ becomes arbitrarily well approximated by the standard normal distribution.
(c)the probability that Y¯ is in the range µY T c becomes arbitrarily close to one as n increases for any constant c > 0. 美国经济学代写
(d) is approximately normal when n is large.
5. The reason why estimators have a sampling distribution is that
(a)economics is not a precise science.
(b)individuals respond differently to incentives.
(c)inreal life you typically get to sample many times.
(d)the values of the explanatory variable and the error term differ acrosssamples
Part B: 美国经济学代写
This year‘s graduating class at Uniform University contains exactly 9OO seniors. Eachsenior has a random number of parents (O, fi, or £) who will attend the graduation ceremony, and it happens that each of those three possibilities is equally likely, with probability fi/3 each, and the numbers of parents attending the ceremony for different seniors are independent random variables. The seating area for parents in the auditorium has 9OO seats. Use a Normal approximation to approximate the probability that all of the parents who attend will be able to be seated. What if the seating area has 9£† seats? What is the minimum number of seats that can ensure that with probability O.9† all of the parents who attend will be able to be seated?
Part C: Let Efi and EX be iid random variables with
for i = 1 and 2.
- What is the mean of Xi? What is the standard deviation of Xi ?2.What is the mean of E¯X = (X1 ＋X2) /£? What is its standard deviation?
3.What is the distribution of E¯X? Graph the distributions of Efi and E¯X. Is the distribution of E¯X close to be normal? (hint: E¯X can be regarded as the mean of a simple random sample with replacement from the population of four persons with their E‘s equal to £, £, 4, and 6, respetively)
Part D: 美国经济学代写
1. Draw †OO random samples of size 8 from a random number generator from a standard normal distribution. Then increase the sample size to 3£. Finally, increase the sample size to fi£8. Plot histograms of the sampling distributions of (i) the sample mean and (ii) the sample variance, for each of these three sample sizes. Now repeat your experiments for three samples drawn from another parametric distribution of your choice (e.g., a uniform distribution). Discuss the results of your experiments in light of the central limit theorem. 美国经济学代写
2. Your experiments produce ”samples of sample means.™ Compute the mean and variance of the sample means generated by each experiment and compare them to the mean and variance predicted by statistical theory. Does the variance of the sample means (i.e., the sampling variance) decrease with the sample size at the rate predicted by the theory? Does Normality matter for this?