3. (12 pts) Let X1, X2,..., Xn be a random sample from Show that θ-1 Ση1X, is an efficient estimator 3. (12 pts) Let X1, X2,..., Xn be a random sample from Show that θ-1 Ση1X, is an efficient es...
Will thumbs up if done neatly and correctly! 6-7. Let θ > 1 and let X1,X2, ,Xn be a random sample from the distri- bution with probability density function f(x; θ-zind, 1 < x < θ. 6. a) Obtain the maximum likelihood estimator of θ, θ b) Is a consistent estimator of θ? Justify your answer 6-7. Let θ > 1 and let X1,X2, ,Xn be a random sample from the distri- bution with probability density function f(x; θ-zind, 1
Find the maximum likelihood estimator θ(hat) of θ. Let X1,X2,...Xn represent a random sample from each of the distributions having the following pdfs or pmfs: (a) f(x; θ)-m', (b) f(x; θ)-8x9-1,0 < x < 1,0 < θ < 00, zero elsewhere ere-e x! θ < 00, zero elsewhere, where f(0:0) x-0, 1,2, ,0 -1
2. Let X1, X2,. ., Xn be a random sample from a uniform distribution on the interval (0-1,0+1). . Find the method of moment estimator of θ. Is your estimator an unbiased estimator of θ? . Given the following n 5 observations of X, give a point estimate of θ: 6.61 7.70 6.98 8.36 7.26
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
3. Let X1 , X2, . . . , Xn be a randon sample from the distribution with pdf f(r;0) = (1/2)e-z-8,-X < < oo,-oc < θ < oo. Find the maximum likelihood estimator of θ.
Let X1, X2, ..., Xn be a random sample with probability density function a) Is ˜θ unbiased for θ? Explain. b) Is ˜θ consistent for θ? Explain. c) Find the limiting distribution of √ n( ˜θ − θ). need only C,D, and E Let X1, X2, Xn be random sample with probability density function 4. a f(x:0) 0 for 0 〈 x a) Find the expected value of X b) Find the method of moments estimator θ e) Is 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 of size n from the exponential distribution whose pdf is f(x; θ) = (1/θ)e^(−x/θ) , 0 < x < ∞, 0 <θ< ∞. Find the MVUE for θ. Let X1, X2, ... , Xn be a random sample of size n from the exponential distribution whose pdf is f(x; θ) = θe^(−θx) , 0 < x < ∞, 0 <θ< ∞. Find the MVUE for θ.
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.
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.