STA312 H5S代写、代做data、R编程设计调试、代写R代写 Statistics统计、回归、迭代|代做数据库SQL

University of Toronto MississaugaSTA312 H5S: Computational Statistics - Winter 2020Final Project.Instructions:❼ Solve only ONE question.❼ You can solve this project either individually or by a group of two. The solution that comes from agroup is expected to have a higher quality of work.❼ There are some questions in the project that require your input. Forexample, choosing the importance function, the set-up of control variateor target density, etc. I don’t have answers for such questions. Do yourbest to answer with quality, justify your work and with details.❼ In this project, you should use R only when it is required. Any other software willnot be accepted.❼ Start your R codes with the following information: Course Number, Final Project,Question #, Your Last Name, First Name, Student Number. For Example,# Course: STA312# Final Project: # 1# Last Name: ABCD, First Name: XYZW# St. #: 0123456789❼ You may not alter the output (by typing or handwriting anything). Output shouldbe directly copied and pasted to the project where needed. If you do not follow theserules, your assignment will not be accepted.❼ Your project should be presented neatly. Use the following format:– Theoretical questions can be hand-written or typed. Though, I recommendtyped!– Attach the cover page (provided) at the front of your project. (Be sure to fillin/circle all the information required).– Include the question numbers/part letters (1a,b,c, etc.) in your answers.– Do not simply hand in pages of R output without further explanation. Onlyinclude the relevant tables or plots that are asked in each question. Make sureto interpret the results in plain English in terms of the problem, quote relevantnumbers from the output, and give justifications as a part of your solutions.– Do not include unnecessary code or output in the body of the project. At theend, include an appendix with ALL your R code and output.STA312- Instructor: Dr. Luai Al Labadi Page 1 of 5Only general discussion is permitted between students. Youmust hand in solutions in your own words. Do not let otherssee your solutions or your selected article. It is plagiarism (aserious academic offence) to submit solutions in other people’swords (including but not limited to other students, the instructor’s,solutions from previous years or courses, websites, etc).You are responsible for knowing and adhering to the Universityof Toronto’s Code of Behaviour on Academic Matters (see courseoutline).STA312- Instructor: Dr. Luai Al Labadi Page 2 of 5Answer any ONE of the following questions.1. Consider the following two probability density functions:f(x) = 2(x − c1)(c2 − c1)2for c1 andg(x) = 2(c2 − x)(c2 − c1)2for c1 where c1 and c2 are finite real numbers.(a) Show that R c2.(b) Find the cumulative distribution functions F(x) and G(x).(c) Write an algorithm to generate a sample from f(x) using the Inverse-Transform algorithm.(d)STA312 H5S作业代写、代做data课程作业、R编程设计作业调试、代写R实验作业 代写留学生 Statistics Show that if X ∼ f(x), then 1 − X ∼ g(x). Explain how you can use this relationship to generatea sample from g.(e) Show that if X ∼ h(x) = 2x, for 0 (f) Derive the inverse-transform algorithm for generating from a sample from h.(g) Explain how you extend the algorithm in (f) to generate a sample form f and a sample from g.(h) Show that if U1 and U2 are two independent random variable from Uniform[0, 1]. Show that Z =max(U1, U2) has the density h.(i) Use part (h) to propose an algorithm to sample from f and from g.(j) Using R, generate a sample of size 104from f (set c1 = 1, c2 = 5) using the two algorithms in (c) (or(g)) and (i). For the generated samples, plot the relative frequency histogram and the correspondingdensity on the same picture. Report the mean and the variance for each case.(k) Repeat part (j) by replacing f by g.(l) Propose an Acceptance-Rejection algorithm to generate a sample from f for c1 = 1, c2 = 5. Using R,compare this method with the previous two methods. Use an appropriate method for comparison.Which one you recommend and why?STA312- Instructor: Dr. Luai Al Labadi Page 3 of 5be the probability density function of a random variable X and k is a positive constant.(a) Find a Monte Carlo estimation to k. denote this estimator by ˆk. Hint: use importance sampling.Compare with the following densities on −∞ You need to write the explicit formula of the estimator for each case.(b) Using R, for each of the above densities, provide the numerical value of the estimator.(c) Find a Monte Carlo estimation estimate for E[X] and E[X2]. You may use ˆk based on f3. Youneed to write the explicit formula of the estimator. Use R to obtain the numerical values. Estimatethe error in the estimation. Report 95% confidence intervals.(d) Use another variance reduction technique to estimate k. You need to write the explicit formula ofthe estimator. Using R, provide the numerical value of this estimator in (e). Compute the meansquared error of the estimator.(f) Use the Acceptance-Rejection algorithm to generate a sample from f. Plot the relative frequencyhistogram and the corresponding density on the same picture.(j) Find the exact value of k. Hint: Γ(z) = R ∞0xz−1e−xdx.(k) Plot the true density on the same picture in (f).STA312- Instructor: Dr. Luai Al Labadi Page 4 of 53. Consider the data given in the file lifetime.txt.(a) Let X denote the lifetime. Estimate E(X) (provide a confidence interval).(b) Apply nonparametric bootstrap procedure to estimate med(X) and kurtosis(X). Estimate 95%-quantile. Provide appropriate confidence intervals.(c) Verify that data follow an exponential distribution. Find λb¸ , an estimator of λ.(d) Apply parametric bootstrap procedure to estimate med(X), kurtosis(X) and 95%-quantile.(e) Compare values obtained via bootstrap to the theoretical values (based on the estimated λb).Good LuckSTA312- Instructor: Dr. Luai Al Labadi Page 5 of 5转自：http://www.6daixie.com/contents/18/5009.html