1. A statistician has a sample X1, . . . , Xn from N(µ, σ 2). Also, the statis-tician has a sample Y1, . . . , Yk from an exponential distribution with param- eter γ. Suppose that these samples are independent. Find the variance of a random variable Z = 3X̄ − 5Ȳ .2. Let a sample of size n from a distribution with the pdf f(x) be given. What is the pdf of X(1)?3. Let X1, . . . , Xn be independent RVs with Eθ(Xl) = lθ. Consider an es- timator Θ̂ =∑n l=1 alXl. What condition should be imposed on a1, a2, . . . , anso that Θ̂ is an unbiased estimator? 4. Let X1, . . . , Xn be iid Bernoulli with the probability of success θ. Sug-gest the minimal variance unbiased estimator, and then prove, using Cramer- Rao inequality, its efficiency.5. Consider a sample of size n from Unif(α, β). Find (minimal) sufficient statistic for the pair (α, β).6. Consider a sample of size n from Unif(0, θ). Find a method of mo- ments estimator of θ.7. Let we observe a sample X1, . . . , Xn where Xl = θ + Yl, with Yl being iid Expon(λ). Find the MLE of θ. Hint: Do not forget about support of the exponential RV.8. For the problem 7, let θ be given. Find the MLE of cos(λ). 9. Consider a sample of size n from Poisson(λ). Find a method ofmoments estimator for the estimand λ2. 10. Let a sample of size n from N(θ, σ2) be given. A statistician believes
At 111papers.com, we value all our customers, and for that, always strive to ensure that we deliver the best top-quality content that we can. All the processes, from writing, formatting, editing, and submission is 100% original and detail-oriented. With us, you are, therefore, always guaranteed quality work by certified and experienced writing professionals. We take pride in the university homework help services that we provide our customers.
As the best homework help service in the world, 111 Papers ensures that all customers are completely satisfied with the finished product before disbursing payment. You are not obligated to pay for the final product if you aren’t 100% satisfied with the paper. We also provide a money-back guarantee if you don’t feel that your paper was written to your satisfaction. This guarantee is totally transparent and follows all the terms and conditions set by the company.Read more
All products that we deliver are guaranteed to be 100% original. We check for unoriginality on all orders delivered by our writers using the most advanced anti-plagiarism programs in the market. We, therefore, guarantee that all products that we submit to you are 100% original. We have a zero-tolerance policy for copied content. Thanks to our strict no plagiarized work rule, you can submit your homework to your professor without worrying.Read more
TThis is one of the most cherished courtesy services that we provide to help ensure that our customers are completely satisfied with our finished products. Delivering the best final product to our customers takes multiple inputs. 111papers.com prides itself on delivering the best university homework help services in the writing industry. And, in part, our free revision policy is how we do it. What’s more, all our revisions are 100% free without any strings attached.Read more
Client privacy is important to use. We know and understand just how important customers value their privacy and always want to safeguard their personal information. Thus, all the information that you share with us will always remain in safe custody. We will never disclose your personal information to any third party or sell your details to anyone. 111 Papers uses the most sophisticated, top-of-the-line security programs to ensure that our customers’ information is safe and secured.Read more
Placing your order with us means that you agree with the homework help service we provide. We, in turn, will endear to ensure that we do everything we can to deliver the most comprehensive finished product as per your requirements. We will also count on your cooperation to help us deliver on this mandate. Yes, we also need you to ensure that you have the highest-quality paper.Read more