Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive numbe...
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1)
and theta being a positive number.
Is the parameter identifiable?.Compute the maximum likelihood
estimate.
If instead of X1,X2,,, We observe, Y1,Y2,...Yn, where
Yi=1(Xi<=0.5).What distribution does Yi follow?
What is the parameter of this distribution? Compute MLE and the
method of moments and Fisher information.
Homework Answers
Add Answer to:
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive numbe...
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive number....
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive number. Is the parameter identifiable?.Compute the maximum likelihood estimate. If instead of X1,X2,,, We observe, Y1,Y2,...Yn, where Yi=1(Xi<=0.5).What distribution does Yi follow? What is the parameter of this distribution? Compute MLE and the method of moments and Fisher information.
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and...
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and X3 ~ N(-1.2). Consider the random column vector X-Xi, X2,X3]T. (a) Write X in the form where Z is a vector of iid standard normal random variables, μ is a 3x vector, and B is a 3 × 3 matrix. (b) What is the covariance matrix of X? (c) Determine the expectation of Yi = Xi + X3. (d) Determine the distribution of Y2...
As on the previous page, let X1,... ,Xn be iid with pdf where θ > 0. (to) 2 Possible points (qual...
As on the previous page, let X1,... ,Xn be iid with pdf where θ > 0. (to) 2 Possible points (qualifiable, hidden results) Assume we do not actually get to observe Xı , . . . , X. . Instead let Yı , . . . , Y, be our observations where Yi = 1 (Xi 0.5) . Our goal is to estimate 0 based on this new data. What distribution does Y follow? First, choose the type of distribution:...
Let X1, X2, ..., Xn be iid with pdf f(x|θ) = θ*x(θ-1). a) Find the Maximum...
Let X1, X2, ..., Xn be iid with
pdf f(x|θ) = θ*x(θ-1). a) Find the Maximum Likelihood
Estimator of θ, and b) show that its variance converges to
0 as n approaches infinity.
I have no problem with part a, finding the MLE of θ. However,
I'm having some trouble with finding the variance.
The professor walked us through part b generally, but I need
help with univariate transformation for sigma(-ln(xi))
(see picture below - the professor used Y=sigma(-ln(x)), and...
Suppose that X1,X2,. X are iid random variables with pdf ,220 (a) Find the maximum likelihood...
Suppose that X1,X2,. X are iid random variables with pdf ,220 (a) Find the maximum likelihood estimate of the parameter a (b) Find the Fisher Information of X1,X2,.. ., Xn and use it to estimate a 95% confidence interval on the MLE of a (c) Explain how the central limit theorem relates to (b).
Suppose that X1, X2, ..., Xn is an iid sample, each with probability p of being...
Suppose that X1, X2, ..., Xn is an iid sample, each with probability p of being distributed as uniform over (-1/2,1/2) and with probability 1 - p of being distributed as uniform over (a) Find the cumulative distribution function (cdf) and the probability density function (pdf) of X1 (b) Find the maximum likelihood estimator (MLE) of p. c) Find another estimator of p using the method of moments (MOM)
Suppose X1, X2, , Xn is an iid sample from a uniform distribution over (θ, θΗθ!),...
Suppose X1, X2, , Xn is an iid sample from a uniform distribution over (θ, θΗθ!), where (a) Find the method of moments estimator of θ (b) Find the maximum likelihood estimator (MLE) of θ. (c) Is the MLE of θ a consistent estimator of θ? Explain.
4. Let X1, X2, ..., Xn be iid from the Bernoulli distribution with common probability mass...
4. Let X1, X2, ..., Xn be iid from the Bernoulli distribution with common probability mass function Px(x) = p*(1 – p)1-x for x = 0,1, and 0 < p < 1 14 a. (4) Find the MLE Ôule of p.
Suppose that (X1, X2,,,,Xn) are iid random variables. Find the maximum likelihood estimator of theta for...
Suppose that (X1, X2,,,,Xn) are iid random variables. Find the maximum likelihood estimator of theta for the following distributions 1) Poi(theta) 2) N(Mu, theta) 3) Exp(theta)
Let X1,X2,...,Xn denote a random sample from the Rayleigh distribution given by f(x) = ...
Let X1,X2,...,Xn denote a random sample from the Rayleigh distribution given by f(x) = (2x θ)e−x2 θ x > 0; 0, elsewhere with unknown parameter θ > 0. (A) Find the maximum likelihood estimator ˆ θ of θ. (B) If we observer the values x1 = 0.5, x2 = 1.3, and x3 = 1.7, find the maximum likelihood estimate of θ.
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and X3 ~ N(-1.2). Consider the random column vector X-Xi, X2,X3]T. (a) Write X in the form where Z is a vector of iid standard normal random variables, μ is a 3x vector, and B is a 3 × 3 matrix. (b) What is the covariance matrix of X? (c) Determine the expectation of Yi = Xi + X3. (d) Determine the distribution of Y2...
As on the previous page, let X1,... ,Xn be iid with pdf where θ > 0. (to) 2 Possible points (qualifiable, hidden results) Assume we do not actually get to observe Xı , . . . , X. . Instead let Yı , . . . , Y, be our observations where Yi = 1 (Xi 0.5) . Our goal is to estimate 0 based on this new data. What distribution does Y follow? First, choose the type of distribution:...
Let X1, X2, ..., Xn be iid with
pdf f(x|θ) = θ*x(θ-1). a) Find the Maximum Likelihood
Estimator of θ, and b) show that its variance converges to
0 as n approaches infinity.
I have no problem with part a, finding the MLE of θ. However,
I'm having some trouble with finding the variance.
The professor walked us through part b generally, but I need
help with univariate transformation for sigma(-ln(xi))
(see picture below - the professor used Y=sigma(-ln(x)), and...
Suppose that X1,X2,. X are iid random variables with pdf ,220 (a) Find the maximum likelihood estimate of the parameter a (b) Find the Fisher Information of X1,X2,.. ., Xn and use it to estimate a 95% confidence interval on the MLE of a (c) Explain how the central limit theorem relates to (b).
Suppose that X1, X2, ..., Xn is an iid sample, each with probability p of being distributed as uniform over (-1/2,1/2) and with probability 1 - p of being distributed as uniform over (a) Find the cumulative distribution function (cdf) and the probability density function (pdf) of X1 (b) Find the maximum likelihood estimator (MLE) of p. c) Find another estimator of p using the method of moments (MOM)
Suppose X1, X2, , Xn is an iid sample from a uniform distribution over (θ, θΗθ!), where (a) Find the method of moments estimator of θ (b) Find the maximum likelihood estimator (MLE) of θ. (c) Is the MLE of θ a consistent estimator of θ? Explain.
4. Let X1, X2, ..., Xn be iid from the Bernoulli distribution with common probability mass function Px(x) = p*(1 – p)1-x for x = 0,1, and 0 < p < 1 14 a. (4) Find the MLE Ôule of p.
Most questions answered within 3 hours.
-
Montecino Corporation uses two different types of labor to
manufacture its product. The types of labor,...
asked 7 minutes ago -
4. What are the two possible products of the
intramolecular hemiacetal formation of linear glucose?
5. ...
asked 29 minutes ago -
The opportunity cost of attending university is likely to
include all except which of the following?...
asked 31 minutes ago -
Consider the following regular
expression: (a*bc+d*e)*
Transform this regular expression to an NFA, from
there to...
asked 28 minutes ago -
1. The Janjua Company had the following account balances at
1/1/16: Common Stock $50,000 Treasury Stock...
asked 29 minutes ago -
A solution with maximum solute that can dissolve and remain
stable is
saturated
unsaturated
miscible
supersaturated
asked 34 minutes ago -
Describe how you would make 100ml of a 10mmol glucose
standard
asked 34 minutes ago -
Zahn Corp.'s comparative balance sheet at December 31, 20x5 and
20x4, reported accumulated depreciation balances of...
asked 34 minutes ago -
How many milliliters of 5.6 M NaOH are needed to neutralize 3.9
mL of a 6.6...
asked 46 minutes ago -
Will dislike
if you don't code efficiently, you must have knowledge of
next.js,vue.js,immutable.js,react,js.
Develop an api...
asked 52 minutes ago -
When financial statements are converted to percentages, they are
referred to as:
A. Percent of change...
asked 52 minutes ago -
16) Which of the following is not a way to reduce the
government's budget
deficit
A)...
asked 1 hour ago