Let X₁,..., Xn be a random sample of size n from the U(0, 0) distribution, where @ > 0is an unknown parameter. Recall that the pdf fof the U(0, 0) distribution is of the formf(x) = { 0-1if 0 < x < 0otherwise.Note that the information about contained in the random sample X₁, Xn equals theinformation about contained in the statisticT = max(X₁, ..',Xn).To understand why so, let's think of the random sample as being obtained in a sequentialmanner, that is, you obtain X₁ and pause before obtaining X₂. What does X₁ tell youabout? It tells you that > X₁. Once you have X₁ and the information that > X₁,obtain X₂. If X₂ > X₁, then you know a bit more about 8, namely, 0 > X₂; however, ifX2 X₁, then it does not contribute anything, above and beyond what you already knowfrom X₁, to your knowledge about 0. In other words, when you have obtained X₁ andX2, what you know about is that it is greater than the maximum of X₁ and X2₂. As such,any reasonable estimator of should be a function of T.(c) Construct an unbiased estimator of which is a function of T and calculate itsvariance. To start with, you should calculate, in that order, the cdf, the pdf, the expectedvalue, and the variance of T.(d) Now consider a biased estimator of 0 of the form cT. Find c* that minimizes the MSEin the class of estimators of the form cT and explicitly verify that the MSE of c*T is lessthan that of the estimator constructed in part (c).

Given that be a random sample of size from the distribution, where is an unknown parameter.

Answered: Let X₁, Xn be a random sample of size n…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 1E

See similar textbooks

Similar questions

Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.
Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is
Let x1, .. , Xn be a random sample with pdf is given by f(x) = {0(1+x)-(1+0), 0, x> 0 otherwise. Find the MLE .
Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 froma distribution having the pdf f(x) = 2x, 0 < x < 1, zero elsewhere. Show thatZ1 = Y1/Y2, Z2 = Y2/Y3, and Z3 = Y3 are mutually independent.
Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.
Let Y, represent the th normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Y₁, Y2. Yin, of size n₁, from the ith population with sample mean Y, and sample variance S² = ₁₁-1(Y₁-₁². j=1 (g) For non-zero constants a's, what is the distribution of U₂ = a₁Y₁-a₂Y₂? State all the relevant parameters of the distribution. (h) Find the standard error of U₂ in part (g), assuming that of = 0² = 0². (i) Discuss how the distribution of Y₁ - ₂ can be used to test the equality of the two population means, #₁ and μ2, when o² = 0 = 0² is known. (j) Define appropriate rejection regions, in terms of Y₁ - Y2, for testing Ho: #₁ = 2 against a two-sided alternative hypothesis at the a level of significance.
Develop a random variate generator for a random variable X with the pdf if 0
Let X be a continuous random variable with pdf
Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf f(x, y) ĮK(x? + y?) 21 25). (Round your answer to three decimal places.) P(Y > 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal 410,600 places.) expected pressure psi standard deviation psi
Let x1,x2,..x n be an jid sample with pdf f(x|0)=0X (® -1) OSxs1,0>0 Find the MLE of 0.
Q3) Let X1,X2,. X, be a random sample from the truncated exponential distribution with pdf: f(x,0) = Please else (a) Derive the method of moment estimator of 0; (b) Derive the MLE of 0. (c) Are the MOME and the MLE unbiased estimators for 0? (d) Compare the MSE of the MOME and the MLE for 0. Which one is a better estimator for 0
Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.

SEE MORE QUESTIONS

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

SEE MORE TEXTBOOKS

Let X₁, Xn be a random sample of size n from the U(0, 0) distribution, where > 0 is an unknown parameter. Recall that the pdf fof the U(0, 0) distribution is of the form [0-¹ f(x) = { {0¹ if 0