TOPIC: Finding the unbiased estimator of the variance of Y based on the given estimator.
(2) Let Y be a binomial random variable with parameters n and p. Remember that We...
(2) Let Y be a binomial random variable with parameters n and p. Remember that E(Y) V(Y)p1 -p) We know that Y/n is an unbiased estimator of p. Now we want to estimate the variance of Y with n(2(1 (a) Find the expected value of this estimator (b) Find an unbiased estimator that is a simple modification of the proposed estimator
Problem 5. Let X be a binomial random variable with parameters n and p. Suppose that we want to generate a random variable Y whose probability mass function is the same as the conditional mass function of X given X-k, for some k-n. Let a = P(X-k), and suppose that the value of a has been computed (a) Give the inverse transform method for generating Y. (b) Give a second method for generating Y (c) For what values of a,...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning. I have no clue how to do these. I know the image quality is iffy but please help as best you can 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...
Please answer as neatly as possible. Much thanks in advance! 7. If Y has a binomial distribution with parameters n and p, consider p = (Y + 1)/(n+2) as an estimator of p. Is p a consistent estimator for p? Is p an asymptotically unbiased estimator for p? 7. If Y has a binomial distribution with parameters n and p, consider p = (Y + 1)/(n+2) as an estimator of p. Is p a consistent estimator for p? Is p...
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...
If Y is a binomial random variable with parameters n=60 and p=0.5, estimate the probability that Y will equal or exceed 45 using the Normal approximation with a continuity correction.
Let X1, X2, .., Xn be a random sample from Binomial(1,p) (i.e. n Bernoulli trials). Thus, п Y- ΣΧ i=1 is Binomial (n,p). a. Show that X = ± i is an unbiased estimator of p. Р(1-р) b. Show that Var(X) X(1-X (п —. c. Show that E P(1-р) d. Find the value of c so that cX(1-X) is an unbiased estimator of Var(X): п
Let N be a binomial random variable with p = 0.2 and n = 10. We roll a fair die N times, let X be the number of times we roll the number 1. Find the joint probability mass function of N and X.
Let M have a binomial distribution with parameters N and p. Conditioned on M, the random variable X has a binomial distribution with parameters M and (a) Determine the marginal distribution for X (b) Determine the covariance between X and Y M- X
2. i) Let B be a random variable with the Binomial (n, p) distribution, so that Write down the likelihood function L(p) for m independent observations xi,...,Inm 2 marks 6 marks ili) Compute the bias and the mean squared error of the corresponding maximum likeli- from B. Int ii) Show that the maximum likelihood estimate for pis-Σ.ri. mn [7 marks] hood estimator of p. iv) Let X be a continuous random variable with density function for x > 0, and...