For n = 20, simulate a random sample of size n from N(μ,22), where μ =...
For n = 20, simulate a random sample of size n from N(μ,22), where μ = 1. Note that we just use μ = 1 to generate the random sample. In the problem below, μ is an unknown parameter. Plot in different figures: (a) the likelihood function of μ, (b) the log likelihood function of μ. Mark in both plots the maximum likelihood estimate of μ from the generated random sample.
Homework Answers
For generating the random sample of given sample size(n=20) the R commands are as follows:
> sample=rnorm(20,mean=1,sd=22)
> sample
[1] -47.6948966 -6.6970829 22.2942976 -28.8633283 4.6385454
-18.5010092
[7] -4.0632007 4.2480641 10.2491721 0.3968407 -51.0694055
6.5430808
[13] -14.5223233 3.1107569 6.5110824 10.4715205 -3.7742037
-12.0635958
[19] 26.5542630 -50.2837780
> plot(sample)
the output are attached below:
Add Answer to:
For n = 20, simulate a random sample of size n from N(μ,22),
where μ =...
R codeing simulation For n = 20, simulate a random sample of size n from N(µ, 2 2 ), where µ = 1....
R codeing simulation
For n = 20, simulate a random
sample of size n from N(µ, 2 2 ), where µ = 1. Note that we just
use µ = 1 to generate the random sample. In the problem below, µ is
an unknown parameter. Plot in different figures: (a) the likelihood
function of µ, (b) the log likelihood function of µ. Mark in both
plots the maximum likelihood estimate of µ from the generated
random sample
(2) For n-20,...
Problem 2. Consider a random sample of size n from a two-parameter distribution with parameter 0...
Problem 2. Consider a random sample of size n from a two-parameter distribution with parameter 0 unknown and parameter η known. The population density function is (xi - T) (a) Find the likelihood function simplifying it as much as possible. Likelihood
Simulate n values of an exponential random variable X with parameter λ (of your choice), and comp...
Simulate n values of an exponential random variable X with parameter λ (of your choice), and compute the sample mean i, sample median m, sample standard deviation s. Plot these quantities as functions of n (on three separate plots). Do x, m, and s converge to any limit values, as n-oo? What are those values and how are they related? Estimate the variance of both x and m for a particular value of n, such as n 100 (by generating,...
Let X1, X2,... X,n be a random sample of size n from a distribution with probability...
Let X1, X2,... X,n be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of λ, λ. Calculate an estimate using this maximum likelihood estimator when 1 0.10, r2 0.20, 0.30, x 0.70.
1. Suppose you are drawing a random sample of size n > 0 from N(μ, σ2)...
1. Suppose you are drawing a random sample of size n > 0 from N(μ, σ2) where σ > 0 is known. Decide if the following statements are true or false and explain your reasoning. Assume our 95% confidence procedure is (X- 1.96X+1.96 Vn a. If (3.2, 5.1) is a 95% CI from a particular random sample, then there is a 95% chance that μ is in this interval. b. If (3.2.5.1) is a 95% CI from a particular random...
(b) Find the natural log of the likelihood function simplifying as much as possible. Loglikelihood =...
(b) Find the natural log of
the likelihood function simplifying as much as possible.
Loglikelihood =
(c) Take the derivative of the log likelihood function you found
in part (b) and make it 0. Solve for the unknown population
parameter as a function of some of the summary statistics we know
(X¯, or S 2 or whatever applies. ) That is your maximum likelihood
estimator (MLE) of the unknown parameter.
PART C ONLY
Problem 2. Consider a random sample of...
Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with...
Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with -∞<μ<∞ and σ2 > 0. a. Develop a likelihood ratio test for H0: μ <= μ0 vs. H1: μ > μ0 b. Develop a likelihood ratio test for H0: μ >= μ0 vs. H1: μ < μ0
Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with...
Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with -∞<μ<∞ and σ2 > 0. a. Develop a likelihood ratio test for H0: μ <= μ0 vs. H1: μ > μ0 b. Develop a likelihood ratio test for H0: μ >= μ0 vs. H1: μ < μ0
QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution,...
QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...
20. Problem 2: (12 points) Let X1, ..., Xn represent a random sample of size n...
20. Problem 2: (12 points) Let X1, ..., Xn represent a random sample of size n from a Rayleigh distribution with parameter 0 and p.d.f. f(0,0) = - , (a) Sow that this is a valid p.d.f. [2] (b) Derive the c.d.f of X. [2] (c) Use the c.d.f of X to obtain the median value of X and interpret it. [2] (d) Find the maximum likelihood estimate of 0. [3] (e) You are now given a random sample of...
R codeing simulation
For n = 20, simulate a random
sample of size n from N(µ, 2 2 ), where µ = 1. Note that we just
use µ = 1 to generate the random sample. In the problem below, µ is
an unknown parameter. Plot in different figures: (a) the likelihood
function of µ, (b) the log likelihood function of µ. Mark in both
plots the maximum likelihood estimate of µ from the generated
random sample
(2) For n-20,...
Problem 2. Consider a random sample of size n from a two-parameter distribution with parameter 0 unknown and parameter η known. The population density function is (xi - T) (a) Find the likelihood function simplifying it as much as possible. Likelihood
Simulate n values of an exponential random variable X with parameter λ (of your choice), and compute the sample mean i, sample median m, sample standard deviation s. Plot these quantities as functions of n (on three separate plots). Do x, m, and s converge to any limit values, as n-oo? What are those values and how are they related? Estimate the variance of both x and m for a particular value of n, such as n 100 (by generating,...
Let X1, X2,... X,n be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of λ, λ. Calculate an estimate using this maximum likelihood estimator when 1 0.10, r2 0.20, 0.30, x 0.70.
1. Suppose you are drawing a random sample of size n > 0 from N(μ, σ2) where σ > 0 is known. Decide if the following statements are true or false and explain your reasoning. Assume our 95% confidence procedure is (X- 1.96X+1.96 Vn a. If (3.2, 5.1) is a 95% CI from a particular random sample, then there is a 95% chance that μ is in this interval. b. If (3.2.5.1) is a 95% CI from a particular random...
(b) Find the natural log of
the likelihood function simplifying as much as possible.
Loglikelihood =
(c) Take the derivative of the log likelihood function you found
in part (b) and make it 0. Solve for the unknown population
parameter as a function of some of the summary statistics we know
(X¯, or S 2 or whatever applies. ) That is your maximum likelihood
estimator (MLE) of the unknown parameter.
PART C ONLY
Problem 2. Consider a random sample of...
QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...
20. Problem 2: (12 points) Let X1, ..., Xn represent a random sample of size n from a Rayleigh distribution with parameter 0 and p.d.f. f(0,0) = - , (a) Sow that this is a valid p.d.f. [2] (b) Derive the c.d.f of X. [2] (c) Use the c.d.f of X to obtain the median value of X and interpret it. [2] (d) Find the maximum likelihood estimate of 0. [3] (e) You are now given a random sample of...
Most questions answered within 3 hours.
-
NASA's Ames Research Center in Mountain View, California, houses
a 20g centrifuge used to conduct research...
asked 34 minutes ago -
I want a python code using recursion ONLY.
I cannot use any loops, dictionaries or modules....
asked 34 minutes ago -
Tobin Supplies Company expects sales next year to be $450,000.
Inventory and accounts receivable will increase...
asked 1 hour ago -
Give the relative rates for the following with a neighbor at your
desk
PH3(g) to P4(g)...
asked 1 hour ago -
Suppose Acap Corporation will pay a dividend of $2.87 per share
at the end of this...
asked 2 hours ago -
Scientists make earthquake forecasts using data from:
A.
geodesy
B.
seismology
C.
geology
D.
paleoseismology
E....
asked 2 hours ago -
Employee training can
be defined as planned organizational efforts to help employees
learn job-related knowledge, skills,...
asked 3 hours ago -
Which for loop is implemented correctly in Java?
Group of answer choices
for (i = 0...
asked 3 hours ago -
Required information
[The following information applies to the questions
displayed below.]
In 2019, Alliant Corporation acquired...
asked 4 hours ago -
How much must I invest today if I want to withdraw 1/3 of my
original investment...
asked 6 hours ago -
What is meant by a “term premium”?
What can explain such a premium? Is it a...
asked 7 hours ago -
23. Which molecule has only covalent bonds? A. CO2 B. Al2O3 C.
Mg3N2
24. The octet...
asked 8 hours ago