Probability Density Function of X is given by:
for 0
x
1,
0 <
< 1
between limits 0 to
Thus, we get:
(1)
Given:
X1, X2, ..., Xn is a random sample
from the population.
Then, Sample mean ()
is given by:
(2)
Equating (1) & (2), we get:
Thus, the method of moments estimator of
is given by:
6. Let X1,..., Xn be a random sample from the pdf Find the method of moments...
6. Let Xi,.Xn be a random sample from the pdf Find the method of moments estimator of θ.
Let X1,..., Xn be a random sample from the pdf f(x:0)-82-2, 0 < θ x < oo. (a) Find the method of moments estimator of θ. (b) Find the maxinum likelihood estimator of θ
5. Let X1, X2,. , Xn be a random sample from a distribution with pdf of f(x) (0+1)x,0< x<1 a. What is the moment estimator for 0 using the method of moments technique? b. What is the MLE for 0?
3. Let X1,... ,Xn be a random sample from a population with pdf 0, otherwise, where θ > 0. (a) Find the method of moments estimator of θ. (b) Find the MLE θ of θ. (c) Find the pdf of θ in (b).
3. Let X1,... ,Xn be a random sample from a population with pdf 0, otherwise, where θ > 0. (a) Find the method of moments estimator of θ. (b) Find the MLE θ of θ. (c) Find the pdf of θ in (b).
5. Let X1, X2, ..., Xn be a random sample from a distribution with pdf of f(x) = (@+1)xº,0<x<1. a. What is the moment estimator for 0 using the method of moments technique? b. What is the MLE for @ ?
5. Let X1,...,Xn be a random sample from the pdf f(\) = 6x-2 where 0 <O<< 0. (a) Find the MLE of e. You need to justify it is a local maximum. (b) Find the method of moments estimator of 0.
Q2: ALL STUDENTS (10 Marks] Let X1, ..., Xn be a random sample from the pdf f(x|0) = 0x-?, O<O<O<0. (a) (3 marks) What is a sufficient statistic for 0? (b) (4 marks) Find the MLE of 0. (c) (3 marks) Find the method of moments estimator of 0.
Let X1,...,xn be a random sample from uniform distribution on the interval (0,). Find the method of moments estimator of . 273X 2X ох none of the answers provided here
Let X1...Xn be a random sample from a continuous distribution with Lomax PDF with gamma=2 a) determine the maximum likelihood estimator of alpha b) determine the estimator of alpha using the method of moments