Let \( Y_1, Y_2, \ldots, Y_n \) denote a random sample from the probability density function\[f(y \mid \theta) = \begin{cases} e^{-(y - \theta)}, & y \geq \theta, \\0, & \text{elsewhere}.\end{cases}\]Show that \( Y_{(1)} = \min(Y_1, Y_2, \ldots, Y_n) \) is sufficient for \( \theta \). **Task:**Find a function of \( Y_{(1)} \) that is an MVUE for \( \theta \).---**Explanation:**- **\( Y_{(1)} \):** This indicates the smallest order statistic from a sample.- **MVUE:** Stands for Minimum Variance Unbiased Estimator, which is an estimator that has the lowest variance among all unbiased estimators for a parameter \( \theta \).In statistical estimation, identifying an MVUE is crucial because it ensures that we estimate parameters as accurately and precisely as possible without systematic error.

Answered: Image /qna-images/answer/ad53c049-4b1b-465a-9de3-c9c6eb9cfb4c.jpg

Answered: Let Y;. Yz. --.. Y, denote a random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

18.) As a measure of intelligence, mice are timed when going through a maze to reach a reward of food. The time (in seconds) required for any mouse is a random variable Y with a probability density function given by fy(y) = y² -& y ≥ b elsewhere where b is the minimum possible time needed to traverse the maze. What is the cumulative distribution function for Y?
Q.2 h(x)==-exp 8 You are given h(x) with the random variable X taking only positive values, -7)+ X 1 X 1 -exp +-expl 2 X 8 24 a. Check if h(x) is a valid pdf (probability density function)? b. Obtain the CDF of X. c. Obtain the mean of X. 4 -exp 80 X 10 ,x≥0
Let f, g be probability densities such supp(f) c supp(g). show yes i.i.d. X1,..., X, L(g) then f(X;) Wi g(X;) is hopeful 1. Argue why the weights need to be re-normalized even when the normalization constants of the densities f and g are known.
2) Consider the random variable Y has a normal distribution with the following probability density function 1 -y?+44y–484 18 f(y) 3/27 0 < y < a) What is the mean and variance of Y? b) What is the median of Y?
let X and Y are two random variables with p.d.f as f(x,y)=3x2y+3yx2 0<x<1 0<x<1.find conditional density of X given Y?.Find mean mode and standard deviation of r.v Y?. Correlation between X and Y?. check that X and Y are independent or not?.
Let μx and of be the expectation and variance of a forecast model F for an observations y, and let pÃ(.) denote the probability density function for the forecast model. Also let G be a different forecast model. Which of the following statements are true? a. Two forecast scores S(F, y) and S(G, y) are independent. b. The square error (y – µµ)² is a proper score. C. The score (y - μF) ²/0 is proper score that improves in the squared error score by taking the variance into account. d. The logarithmic score – log[pf(y)] is a strictly proper score. -
Let W₁ < W₂ < ... < Wn be the order statistics of n independent observations from a U(0, 1) distribution. (a) Find the pdf of W₁ and that of Wn. (b) Use the results of (a) to verify that E (W₁) = 1/(n+1) and E(Wn) = n/(n+1).
5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = I > 0 (x+0)a+1³ is a probability density function. What can you say about the mean of a random variable that has fo,a as a pdf?
6.106 If Y is a continuous random variable with distribution function F(y), find the probability density function of U = F(Y).
2. Consider a gas station's daily sales. Let Y be the volume of gas sold per day in 1000s of gallons. Assume the distribution of Y follows this pdf: 1sxs 2 S (v) . else What value of k is required for the above function to be a valid pdf? b. Verify that the function given is a valid probability density а. function c. Determine the cumulative distribution function (cdf) of the random variable d. Compute the probability that there is exactly 1500 gallons of sales on a given day (Hint: Find?(r - 1.5)) = 1 CO0
*2. Let log Y the median of Y). ~ N (u, o2). Find the distribution of Y and show that P(Y < eH) = 0.5 (i.e., el is
Q1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . . (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

Let Y;. Yz. --.. Y, denote a random sample from the probability density function e , y20, 0, elsewhere. Show that Y1) = min(Y1, Y2, .... Y,) is sufficient for e. %3!