Just D please 2. Suppose that X₁,..., Xn form a random sample from a Exponential(\) distribution, with PDFgiven byf(x|λ) = Ae¯λx for x > 0, λ > 0.In the above form, À is a rate parameter and E(X) = 1/λ and var(X) = 1/λ².(a) Find a MOM (method of moment) estimator Ã of X.(b) Write down the likelihood function Ln (A) and obtain the maximum likelihood estimator(MLE) Â of A.(c) Let 7 denote the population median. Obtain the MLE of T. (Hint: First find the specificform of the median in terms of λ and utilize the invariance property of MLE)(d) Is it easy to study the finite-sample distributional property of the MLE Â, such as E(Â),var(Â), the mean square error (MSE) in estimating \, and its exact sampling distribution?(e) Compute the Fisher information In in the sample data. Accordingly, obtain the asymp-totic distribution of Â.(f) Obtain a sufficient statistic T(X₁,..., X₂) for À via the factorization theorem. Verify thatthe MLE Â is a function of T.

Given that X1, . . ., Xn form a random sample from a Exponentialλ distribution, with PDF fx|λ=λe-λx…

Answered: (d) Is it easy to study the…

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 X₁, X2,..., Xñ be a random sample from the exponential distribution with rate parameter A. (a) Find the CRLB for the variance of all unbiased estimators of X. (b) Find the efficiency of the MLE of X. (c) Find the CRLB for the variance of all unbiased estimators of E(X) = 1/λ. (d) Can you find an estimator of E(X) = 1/λ that is efficient? Justify your answer.
7. Let X be a continuous random variable with pdf f(x)=√ 0
Derive a general expression for the variance of net future loss Var(L) with a constant force of interest δ under each of the following models:i. μ_x(t) = μii. μ_x(t) = 1/(ω-x)
Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1<y<3.(a) Calculate P (Y > 2.5).(b) Calculate the variance of Y .
The pdf is given as follows: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.
A time series dataset consists of 100 observations x, x,., j09. The following summary statistics have been made derived for this data: 100 100 100 E*, = 1,000; (x, - x) = 280;(x, -F)(x-X) = 50:E(-(*-)=-250. a) Calculate the sample autocorrelation functions at lags 1 and 2.
Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.
The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−3/4. Calculate Var(X+Y) with a full explanation
The p.d.f. of a random variable X' is as shown in the figure. The pdf is zero for X 5. Calculate (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X. fx (x) k
t x, x, ... x be a random sample from an exponential distribution with parameter 0. Find sufficient estimator for '8'.

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

(d) Is it easy to study the finite-sample distributional property of the MLE Â, such as E(1), var(Â), the mean square error (MSE) in estimating À, and its exact sampling distribution?