1. Let X1, , Xn be iid with population densityx > 8,fx(x) =otherwise.X-8Here 8,0 are unknown population parameters. You can use the fact that has Exp(1)distribution without proof in this problem.Does the Cramer-Rao lower bound exist for any unbiased estimator 8 of 8? Ifyes find it. If no explain why.Does the Cramer-Rao lower bound exist for any unbiased estimator 0 of 0? Ifyes find it. If no explain why.

Answered: Image /qna-images/answer/7da4da59-e8c7-4c84-9198-9230024c0522.jpg

Let X1,· , Xn be iid with population density x > 8, fx (x) = {de- otherwise. Here d,0 are unknown population parameters. You can use the fact that has Exp(1) distribution without proof in this problem. X-8 Does the Cramer-Rao lower bound exist for any unbiased estimator d of 8? If

Let X1,· , Xn be iid with population density x > 8, fx (x) = {de- otherwise. Here d,0 are unknown population parameters. You can use the fact that has Exp(1) distribution without proof in this problem. X-8 Does the Cramer-Rao lower bound exist for any unbiased estimator d of 8? If

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Suppose that X and Y are independent random variables each with a x'(2) distribution. Find the…

Q: Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown.…

Q: 7) Let X₁, X2,...Xn i.i.d random sample from U(0, 0). Consider two estimators of 6₁ = 2X₂ and 6₂ =…

Q: What is the relative risk for the association between men and women vs COVID-19 infection? What do…

A: Data is given for Men and women, vs Covid infection ( Covid positive and Covid negative We have to…

Q: 29. Suppose X1, X2, X3 are a random sample of size 3 from a distribution with pdf f(x) = (1/0)ex/0…

Q: (2x-x*), 2x-x²), 0<xs2 Suppose X is random variable whose p.d.f. is f(x)={4 0, elsewhere Find the…

A: It is an important part of statistics. It is widely used.

Q: Suppose that Y₁ = B₁ X₁ + €į, i=1,..., n where ~ iid N(0,0²), σ > 0 holds true. We only have the…

A: Given: where εi is normally distributed with mean 0 and variance σ2.a) The likelihood function for…

Q: and they are independent

A: *Answer:

Q: Next question hearts? An experiment consists of dealing 4 cards from a standard 52-card deck. What…

A: no.of heart cards=13total no.of cards=52

Q: (a) What is the method of moment estimator Amom of X? (b) What is the maximum likelihood estimator…

Q: Let Y1, Y2, . . . , Yn ∼ (iid) Exp(γxi) where xi , i = 1, 2, . . . , n and the xi ’s are fixed and…

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi.…

A: Understanding the Pressure Relationship in TiresKnowing the air pressure in one tire of a vehicle…

Q: Let X1, ·.. , X, " f (x;0) = e-=/°, x > 0. (i) Find the sCore and information functions of 0. (i)…

Q: IfX1 andX2 are the means of independent random samples of sizes n1 and n2 from a normal population…

Q: In Step 2, am I supposed to take a second derivative of the log likelihood function and make sure…

Q: Assume that two countries are on the verge of war and are simultaneously deciding whether or not to…

A: There are two type space given where probability of being type Probability of being type,…

Q: Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator…

A: It is given that X ~ Bin( n, θ ) We know that E( X ) = nθ

Q: Let {x .,x } is a random sample coming from N(μ, σ^), and suppose σ is known. (a) Show that hat(e) =…

A: To solve this problem, we need to use the properties of the normal distribution and the concept of…

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

Q: We know that the point estimator o` is an unbiased estimator for the parameter 0 if E(e') = 0.If the…

A: Unbiased estimator: Any statistic is said to be an unbiased estimator of the specified parameter, if…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

1. Let X1, , Xn be iid with population density
x > 8,
fx(x) =
otherwise.
X-8
Here 8,0 are unknown population parameters. You can use the fact that has Exp(1)
distribution without proof in this problem.
Does the Cramer-Rao lower bound exist for any unbiased estimator 8 of 8? If
yes find it. If no explain why.
Does the Cramer-Rao lower bound exist for any unbiased estimator 0 of 0? If
yes find it. If no explain why.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Suppose that X and Y are independent random variables each with a x²(4) distribution. Find the moment generating function of U = X +5Y and evaluate the expectation value E(U). State clearly and justify all steps taken. Hint: You may use without proof the fact that the moment generating function of a x²(v) random variable W is Mur-(t) = (-)". 2t
2 If X₁ and X₂ are the means of independent ran- dom samples of sizes n₁ and n₂ from a normal population with the mean u and the variance o2, show that the vari- ance of the unbiased estimator 2 w X₁ + (1-w). X₂ is a minimum when @ = n1 n₁ + n₂ idnu
I am having a tought time with this question
Please no written by hand solution
(5) If Xis a r.v. with mean u and variance o?, using Chebyshev's-Inequality, AX-2 20) S (a) 0.5 (b) 0.05 (c)0.657 (d) 0.25.
Suppose there are three possible states of nature, and the class-conditional PDFS are the Cauchy distributions 1 p(rw;) = 1 i = 1,2,3. (1) 2 1+ bị Let ai = -2, a2 = 0, az = 2, bị = b2 = 1, b3 = 0.5. Let P(wi) = P(w2) = 0.4, P(w3) = 0.2. (a) Find the decision boundaries and the decision regions for the Bayesian decision (b) Calculate the probability of error for the classification done according to this
Aleem tossed a coin 50 times and recorded the results in a frequency distribution table. Outcome Frequency Heads 22 Tails 28 What is the experimental probability of tossing a head?
Please answer number2