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Question: i figured out 12 and 3 but im stuck on...

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I figured out 1,2 and 3 but I’m stuck on 4 and 5. Please help me out if you can!! I know the quality isn’t the greatest, I’m sorry!!

Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will prepare you for the exam. Please turn in your work in class on Thursday Janaary 24th. If you cant come to class that day, please drop your homework in my mailbox (Griffin Floyd 103) by the time class has begun. (1) The number of persons coming through a blood bank until the finst person with blood type A is found is a random variable Y with a geometric(p) distribution. If p denotes the probability that any one randomly selected person will ponsess type A blood, then E(Y)-1/p and V)- Find a function of Y that is an unbiased estimator of Vy (2) Let Y be a binomial random variable with parameters n and p. Remember that E(Y) = np V(Y)-np(1-P) We know that Y/n is an unbiased estimator of p. Now we want to estimate the variance of Y with n(X - (a) Find the expected value of this estimatos (b) Find an unbiased estimator that is a simple modification of the proposed estimator ^ (3) Suppose that E(4)-θ, E(6) _ θ, l(4)- and V(.)- . Aseume that o, and e, are independent. Consider the following estimator: (a) Show that o, is lanbiased for θ (b) Find the value of a that minimizes the variance of (e) Which estimator would you use? ,or 0, when using the value of a found in part 4) Let Y... Y be N(0,1). Let-Y and (a) what are the possible values of the θ. (b) Find the bias and MSE of both the estimators (c) Is one of the estimators better than the other? (d) Fr what values of θ is better than 02? (5) let ,, Yİ be independent random variables from a distribution with distribution functio P(Y v)-F(y), and density function f(v). Now let Ya, be the minimum of all the olwervations. Show that the density function of Yu is given by [Hint: First write out the CDF. POİ.IS y), then using independence of the observatius put it in terms of the distribution function Fi ..เ d ,hen take the derivative to get the density. 1 of 1
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