Can you please help me to solve the following question 3. Let X1,X2, . . . , Xn be a randoml sample from the distribution with pdf f(x; θ) = (1/2)e-la-9 x < x < oo,-oo < θ < oo. Find the maximum likelihood estimator of θ
3. Let X1, X2, . . . , Xn be a random sample from a distribution with the probability density function f(x; θ) (1/02)Te-x/θ. O < _T < OO, 0 < θ < 00 . Find the MLE θ
Let X1, X2, ..., Xn represent a random sample from each of the distributions having the following pdf. Please find the maximum likelihood estimator for each case: (c) f(x; θ)--e-x/e,0 < x < 00, 0 < θ < oo, zero elsewhere (d) f(x; θ) e- , θ x < 00,-00 < θ < 00, zero elsewhere In each case, find the mie of a (x-6)
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?
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
Let X1, X2,.. Xn be a random sample from a distribution with probability density function f(z | θ) = (g2 + θ) 2,0-1(1-2), 0<x<1.0>0 obtain a method of moments estimator for θ, θ. Calculate an estimate using this estimator when x! = 0.50. r2 = 0.75, хз = 0.85, x4= 0.25.
Let X1, X2, ..., Xn be a random sample from a Gamma( a , ) distribution. That is, f(x;a,0) = loga xa-le-210, 0 < x <co, a>0,0 > 0. Suppose a is known. a. Obtain a method of moments estimator of 0, 0. b. Obtain the maximum likelihood estimator of 0, 0. c. Is O an unbiased estimator for 0 ? Justify your answer. "Hint": E(X) = p. d. Find Var(ë). "Hint": Var(X) = o/n. e. Find MSE(Ô).
3 from the exponential distribu- Let X1,ng and tion with pdf be a randon sample of size n f(x) -4e-4x, 0 < x < oo. Find a. P(0.2< X1,0.2< X2 < 1.5,0.25< X3< 0.8) b. E[2560X1 (X2-0.25)"(Xy-0.25判·
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 @ ?
4. Let X1, X2, ..., Xn be a random sample from a distribution with the probability density function f(x; θ) = (1/2)e-11-01, o < x < oo,-oo < θ < oo. Find the NILE θ.