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:
Homework Answers
here to find the MLE of c we will differentiate the log likelihoid for part c and apply argument method for part d since d cann't be solved by differentiation method. if any doubt ask by comment please and give your good rating to answer please.
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Let X1, X2, ..., Xn represent a
random sample from each of the distributions having the...
Find the maximum likelihood estimator θ(hat) of θ. Let X1,X2,...Xn represent a random sample from each...
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
1.2. Let X 1,X2,. , Xn represent a random sample from each of the distributions having...
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.
3. Let X1 , X2, . . . , Xn be a randon sample from the...
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.
1. Let X1, X2,...,X, be a random sample from each of the distributions having the to...
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,...
6. Let X1, X2,.. , Xn denote a random sample of size n> 1 from a...
6. Let X1, X2,.. , Xn denote a random sample of size n> 1 from a distribution with pdf f(x; 6) = 6e-8, 0<x< 20, zero elsewhere, and 0 > 0. Le Y = x. (a) Show that Y is a sufficient and complete statistics for . (b) Prove that (n-1)/Y is an unbiased estimator of 0.
3. Let X1, X2, . . . , Xn be a random sample from a distribution...
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,..., Xn be a random sample from the pdf f(x:0)-82-2, 0 < θ x <...
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
l. Find the maxinum likelihood estimator (MLE) of θ based on a random sample X1 ,...
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, ..., Xn be a random sample from a population with pdf f(x 1/8,0 <...
Let X1, ..., Xn be a random sample from a population with pdf f(x 1/8,0 < x < θ, zero elsewhere. Let Yi < < Y, be the order statistics. Show that Y/Yn and Yn are independent random variables
Let X1, X2, ..., Xn be a random sample from a Gamma( a , ) distribution....
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).
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
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.
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.
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,...
6. Let X1, X2,.. , Xn denote a random sample of size n> 1 from a distribution with pdf f(x; 6) = 6e-8, 0<x< 20, zero elsewhere, and 0 > 0. Le Y = x. (a) Show that Y is a sufficient and complete statistics for . (b) Prove that (n-1)/Y is an unbiased estimator of 0.
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,..., 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
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, ..., Xn be a random sample from a population with pdf f(x 1/8,0 < x < θ, zero elsewhere. Let Yi < < Y, be the order statistics. Show that Y/Yn and Yn are independent random variables
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).
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