Find the maximum likelihood estimator θ(hat) of θ.
Find the maximum likelihood estimator θ(hat) of θ. Let X1,X2,...Xn represent a random sample from each...
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)
1.2. Let X 1,X2,. , Xn represent a random sample from each of the distributions having the following pdfs: (a) f(x:0-829-1, 0 < x < 1, 0 < θ < oo, zero elsewhere. (b) f(x:0) = e-u-0), θ S1 < oo,-oo < θ < oo, zero elsewhere. Note this is a nonregular case. In each case find the mile θ of θ.
1. Let X1, X2,...,X, be a random sample from each of the distributions having the to lowing pdfs or pmfs: (a) f(x; 0) = 6"e-/x!, r = 0,1,2, ..., 0< < oo, zero elsewhere, where f(0,0) = 1. (b) f(2; 6) = 0.00-110,1)(2), 0 <O< 0o. (c) f(x; 6) = (1/0)e-1/10,00) (2), 0 <$<. (d) f(x; 0) = e-(2-) 110,00) (2), - < < . • For each case, find the ML estimator ômle of 0; • For each case,...
l. Find the maxinum likelihood estimator (MLE) of θ based on a random sample X1 , xn fronn each of the following distributions (a) f(x:0)-θ(1-0)z-1 , X-1, 2, . . . . 0 θ < 1
Let X1, X2, ..., Xn denote a random sample of size n from a population whose density fucntion is given by 383x-4 f S x f(x) = 0 elsewhere where ß > 0 is unknown. Consider the estimator ß = min(X1, X2, ...,Xn). Derive the bias of the estimator ß.
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 estimator
Let X1,X2,...,Xn denote a random sample from the Rayleigh distribution given by f(x) = (2x θ)e−x2 θ x > 0; 0, elsewhere with unknown parameter θ > 0. (A) Find the maximum likelihood estimator ˆ θ of θ. (B) If we observer the values x1 = 0.5, x2 = 1.3, and x3 = 1.7, find the maximum likelihood estimate of θ.
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
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
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