Hello,
The sufficient statistics would rather be . You can't isolate itself.
Please do the caculations again, the MLE is something like
And it will indeed be unbiased since the expectation of the texponential distribution is 1/(k*lambda)
X1, X2, .... ,Xn are independet exponential random variables with E(Xk)=k times lambda where k = 1,2,...,n. What is the sufficient statistics and maximum likelihood estimators of lambda??? and is it unbiased?
(a) sufficient statistics i got summation of Xk where k is from 1 to n
(b) MLE i got (1/n) times summation (Xk)/k where k is from 1 to n
(c) it is unbiased
Is my answers all correct??please reply me..thank you!!
Hello,
The sufficient statistics would rather be . You can't isolate itself.
Please do the caculations again, the MLE is something like
And it will indeed be unbiased since the expectation of the texponential distribution is 1/(k*lambda)
I have another problem. Let X1,X2,...,Xn be a random sample of size n from a distribution with density function f(x;theta) = c2^[-(x-theta)^2]. if theta is known, the MLE of c is infinity is it?? i formed the likelihood function and take the derivative of the ln of the function then let it equal to zero.
oh..but the question is like that..i think i just stick to my answer which is infinity. And i wanna ask if i want to find the 95% confidence interval of theta, after i found the estimator of theta, how to find the distribution of it?