2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...

Question

Question

2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x) = or-(-) where x 2 1 a

2.4 Show that the fisher information in the whole sample is: In(a)=

2.5 What Cramer Rao lower bound for unbiased estimators of a?

2.7 Consider estimating the unknown quantity: g(a) = 0 - 4+.. Determine the MLE of gla). What property are you using to justi

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

2-4) Formula? In(a): NECTA Więce)] -- EL [a z te=]] « [ d² enx lmassa dar lux da² z n -n [az] (86/1,6) 2:5) By definition & C

Add a comment

Answer 2

Similar Homework Help Questions

2 Let X, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...

2 Let X, X2, ..., X, be independent continuous random variables from the following distribution: f(x) - ar"(-) where 2 2 1 and a > 1 You may use the fact: EX- 2.4 Show that the fisher information in the whole sample is: In(a) = 2.5 What Cramer Rao lower bound for unbiased estimators of a? 2.7 Consider estimating the unknown quantity: 9(a) = alet. Determine the MLE of g(a). What property are you using to justify your answer?
2 Let X1, X2, ...,X, be independent continuous random variables from the following distribution: f(3) =...

2 Let X1, X2, ...,X, be independent continuous random variables from the following distribution: f(3) = ox-(0-1) where : > 1 and a > 1 You may use the fact: E[X]- .- 2.1 Show that the maximum likelihood estimator of a is ômle = Ei log Xi 2.3 Derive a sufficient statistic for a. What theorem are you using to determine sufficiency? 2.4 Show that the fisher information in the whole sample is: 1(a)= 2.5 What Cramer Rao lower bound...
2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: (*)...

2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: (*) - ar-(-) where I 21 and a > 1 You may use the fact: E[X] = -1 2.1 Show that the maximum likelihood estimator of a is â MLE - Srlos Xi 2.2 Show that the method moment estimator for a is: &mom = 1 2.3 Derive a sufficient statistic for a. What theorem are you using to determine sufficiency?

Let X1,X2,...,Xn be iid exponential random variables with unknown mean β. (b) Find the maximum likelihood...

Let X1,X2,...,Xn be iid exponential random variables with unknown mean β. (b) Find the maximum likelihood estimator of β. (c) Determine whether the maximum likelihood estimator is unbiased for β. (d) Find the mean squared error of the maximum likelihood estimator of β. (e) Find the Cramer-Rao lower bound for the variances of unbiased estimators of β. (f) What is the UMVUE (uniformly minimum variance unbiased estimator) of β? What is your reason? (g) Determine the asymptotic distribution of the...
Let X1, X2, ..., Xn be a random sample from the distribution with pdf f(3;6) =...

Let X1, X2, ..., Xn be a random sample from the distribution with pdf f(3;6) = V porta exp ( 0) 10.02) for some parameter 2 > 0. (a) Find the MLE for 0. (b) Find the Cramér-Rao lower bound for the variance of all unbiased estimators of 0. (c) Find the asymptotic distribution of your MLE from part (a).
2 Let X1, X2, ..., X., be independent continuous random variables from the following distribution: f(x)=ox-(-V...

2 Let X1, X2, ..., X., be independent continuous random variables from the following distribution: f(x)=ox-(-V where = 1 and a > 1 You may use the fact: E(X)= -1 2.1 Show that the maximum likelihood estimator of a isante = sok X. 2.2 Show that the method moment estimator for a is: & mom = 1 2.3 Derive a sufficient statistic for a. What theorem are you using to determine sufficiency?

Let X1, . . . , Xn be a random sample from a population X with...

Let X1, . . . , Xn be a random sample from a population X with p.d.f fθ(x) =    θ xθ−1 , for 0 < x < 1 0, otherwise, where θ > 1 is parameter. Find the MLE of 1/θ. If it is an unbiased estimator of 1/θ, compare its variance with the Cramer-Rao lower bound.
Solve the problem with all necessary steps in detail. 30 points) Let X1, X2, ..., Xybe...

Solve the problem with all necessary steps in detail. 30 points) Let X1, X2, ..., Xybe independent, identically distributed random variables with p.d.f. f(x) = 22,0 sxso. a. Let Yn be the maximum value of the sample. Is this an unbiased estimator for @? If not, find a constant c so that co is an unbiased estimator. b. Calculate (0) and the Cramer-Rao lower bound for the variance of an unbiased estimator for e. C. Find the variance of the...
7. Let X1,....Xn random sample from a Bernoulli distribution with parameter p. A random variable X...

7. Let X1,....Xn random sample from a Bernoulli distribution with parameter p. A random variable X with Bernoulli distribution has a probability mass function (pmf) of with E(X) = p and Var(X) = p(1-p). (a) Find the method of moments (MOM) estimator of p. (b) Find a sufficient statistic for p. (Hint: Be careful when you write the joint pmf. Don't forget to sum the whole power of each term, that is, for the second term you will have (1...

Question 3 15 marks] Let X1,..,X be independent identically distributed random variables with pdf common )...

Question 3 15 marks] Let X1,..,X be independent identically distributed random variables with pdf common ) = { (#)%2-1/64 0 fx (a;e) 0 where 0 >0 is an unknown parameter X-1. Show that Y ~ T (}, ); (a) Let Y (b) Show that 1 T n =1 is an unbiased estimator of 0-1 ewhere / (0; X) is the log- likeliho od function; (c) Compute U - (d) What functions T (0) have unbiased estimators that attain the relevant...

2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...

Homework Answers

Add Answer to:
2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...

Post as a guest

Earn Coins

2 Let X, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...

2 Let X1, X2, ...,X, be independent continuous random variables from the following distribution: f(3) =...

2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: (*)...

Let X1,X2,...,Xn be iid exponential random variables with unknown mean β. (b) Find the maximum likelihood...

Let X1, X2, ..., Xn be a random sample from the distribution with pdf f(3;6) =...

2 Let X1, X2, ..., X., be independent continuous random variables from the following distribution: f(x)=ox-(-V...

Let X1, . . . , Xn be a random sample from a population X with...

Solve the problem with all necessary steps in detail. 30 points) Let X1, X2, ..., Xybe...

7. Let X1,....Xn random sample from a Bernoulli distribution with parameter p. A random variable X...

Question 3 15 marks] Let X1,..,X be independent identically distributed random variables with pdf common )...

2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...

Homework Answers

Add Answer to: 2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...

Post as a guest

Earn Coins

Add Answer to:
2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...