7.7.4 As in Problem 7.6.3, let X₁,..., X be a set of independent random variables with a U(0, 0)distribution, and letT= max{X₁,..., X₂}Explain why the likelihood function L(x₁,..., Xn, 0) is equal toif 0 > t = max {x,...,xn), and is equal to 0 otherwise.Sketch the likelihood function against 0, and deduce that the maximum likelihood estimate of 0 is Ô =t. What is the bias of this point estimate?

A random sample X1,...., Xn of size 'n' is taken from a distribution U0,θ. The PDF of X is given by:…

Answered: 4 As in Problem 7.6.3, let X₁,..., X be…

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

Similar questions

2. If x is a value assumed by a random variable X having the exponential distribution given by x > 0, elsewhere f(x)= = 0 >0 Ө 0, Find k so that the interval 0 <0
a) Let X₁, X2,..., X be a random sample of size n from population X. Suppose that X has the following probability mass function: (0(1-0)*-1, (o, i) Find the conditional distribution of the likelihood function given the function of the statistic, 6 = ₁X₁. Hint: Apply f(L(0)|g(0,0)). ii) Based on i) above, is = 1X₁ a sufficient statistic? Justify your answer. B ii) Show whether or not X, is a consistent estimator of the parameter f(x; 0) = x = 1,2,3,... elsewhere
2) Let X₁, X2, X3, X4 be a random sample of size 4 from a population with the following distribution function Where, ß > 0. If fram e ¹- {** f(x;0)=B for x > 4 otherwise "1 g) What is the maximum likelihood estimator of g (B) = 2(ß + 1). h) Is the maximum likelihood estimator of g (B) = 2(B + 1) unbiased or not?
9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: (f(x|y = 1)
Question 3. Let X₁,, Xn be a random sample from a distribution with the pdf given by f₁₁x(x) = exp(-ª) if x ≥ A, otherwise f(x) = 0, where > 0. Find the MLE's of 0 and X. Start by writing the likelihood function and note the constraint involving A. Question 4. #4.2.9 of the textbook.
Please help me for Question 2
3. If x1, X2, X3, ..., Xn is a random sample from a normal 1 distribution N (µ, 1) show that t= E xí is an unbiased estimator of n i = 1 H² + 1.
11. Let (y1, Y2 ... Yn) be independent random sample from the uniform distribution on [0, 1]. (a) show that Z = – In Y; has exponential distribution with parameter 1. (b) Hence or otherwise, show that -2 In Y; xản
10. Two random variables X and Y take on the values i and 2 with probability 1/2' (i = 1,2, ...). Show that the probabilities sum to one. Find the expected value of X and Y.
Please no written by hand solution
7. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: The marginal function of x %3D
If the roots of the quadratic equation x – ax + b = 0 are real and b is positive but otherwise unknown, what are the expected values of the roots of the equation. Assume that b has a uniform distribution in the permissible range. -

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS