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8(100) Let X1,,Xn be iid from r(a, 6). (1)(50) Find the limiting distribution of the MLE of B. (2)(30) Find the lim...
4.(120) Let X1,,,Xn be iid r(, 1) and g(u) given. Let 6n be the MLE of g(4) (1)(60) Find the asymptotic distributio...
4.(120) Let X1,,,Xn be iid r(, 1) and g(u) given. Let 6n be the MLE of g(4) (1)(60) Find the asymptotic distribution of 6, (2)(60) Find the ARE of T Icc(X) w.r.t. on P(X1> c), c > 0 is i n i1 5.(80) Let X1, ,,Xn be iid with E(X1) = u and Var(X1) limiting distribution of nlog (1 +). o2. Find the where T n(X - 4)/s. - 1 -
4.(120) Let X1,,,Xn be iid r(, 1) and g(u)...
Let X1, X2, ..., Xn be iid random variables from a Uniform(-0,0) distribution, where 8 >...
Let X1, X2, ..., Xn be iid random variables from a Uniform(-0,0) distribution, where 8 > 0. Find the MLE of 0.4
3. Let X1, ..., Xn, ... be iid random variables from the shifted exponential distribution: Se-(2-0)...
3. Let X1, ..., Xn, ... be iid random variables from the shifted exponential distribution: Se-(2-0) f( x0) = л VI (a) Find the MLE for 0. (b) Find the MLE for ø= EX. (c) Find the MOM estimator for 0.
Let X1, . . . , Xn ∼ iid N(θ, σ^2 ), where σ^2 is known....
Let X1, . . . , Xn ∼ iid N(θ, σ^2 ), where σ^2 is known. We wish to estimate φ = θ^2 . Find the MLE for φ and the UMVUE for φ. Then compare the bias and mean squared error's of the two estimators
iid 20. Let X1, ...,Xn - Exp(a), the exponential distribution with failure rate 2. We showed...
iid 20. Let X1, ...,Xn - Exp(a), the exponential distribution with failure rate 2. We showed in Sections 7.2 and 7.3 that â= 1/X is both the MME and the MLE of 2, and that its asymp- totic distribution is given by vn (Å - 1) PW~N (0,22) (8.53) Use the normal distribution in (8.53) to obtain, via a variance stabilizing transformation, an approximate 100(1 – a)% confidence interval for a.
4. Let X1, X2, ..., Xn be iid from the Bernoulli distribution with common probability mass...
4. Let X1, X2, ..., Xn be iid from the Bernoulli distribution with common probability mass function Px(x) = p*(1 – p)1-x for x = 0,1, and 0 < p < 1 14 a. (4) Find the MLE Ôule of p.
Let X1, . . . , Xn ∼ iid Unif(θ − 1/2 , θ + 1/2...
Let X1, . . . , Xn ∼ iid Unif(θ − 1/2 , θ + 1/2 ) for θ unknown. Find an asymptotic confidence interval for θ.
Again, let X1,..., Xn be iid observations from the Uniform(0,0) distribution. (a) Find the joint pdf...
Again, let X1,..., Xn be iid observations from the Uniform(0,0) distribution. (a) Find the joint pdf of Xi) and X(n)- (b) Define R = X(n)-X(1) as the sample range. Find the pdf of R. (c) It turns out, if Xi, . . . , xn (iid) Uniform(0,0), E(R)-θ . What happens to E® as n increases? Briefly explain in words why this makes sense intuitively.
Let X1, ..., Xn be IID observations from Uniform(0, θ). T(X) = max(X1, . . ....
Let X1, ..., Xn be IID observations from Uniform(0, θ). T(X) = max(X1, . . . Xn) is a sufficient statistic (additionally, T is the MLE for θ). Find a (1 − α)-level confidence interval for θ. [Note: The support of this distribution changes depending on the value of θ, so we cannot use Fisher’s approximation for the MLE because not all of the regularity assumptions hold.]
Let X1, . . . , Xn ∼ iid Unif(θ − 1/2 , θ + 1/2 ) for θ unknown. Find an asymptotic confidence in...
Let X1, . . . , Xn ∼ iid Unif(θ − 1/2 , θ + 1/2 ) for θ unknown. Find an asymptotic confidence interval for θ.
4.(120) Let X1,,,Xn be iid r(, 1) and g(u) given. Let 6n be the MLE of g(4) (1)(60) Find the asymptotic distribution of 6, (2)(60) Find the ARE of T Icc(X) w.r.t. on P(X1> c), c > 0 is i n i1 5.(80) Let X1, ,,Xn be iid with E(X1) = u and Var(X1) limiting distribution of nlog (1 +). o2. Find the where T n(X - 4)/s. - 1 -
4.(120) Let X1,,,Xn be iid r(, 1) and g(u)...
Let X1, X2, ..., Xn be iid random variables from a Uniform(-0,0) distribution, where 8 > 0. Find the MLE of 0.4
3. Let X1, ..., Xn, ... be iid random variables from the shifted exponential distribution: Se-(2-0) f( x0) = л VI (a) Find the MLE for 0. (b) Find the MLE for ø= EX. (c) Find the MOM estimator for 0.
iid 20. Let X1, ...,Xn - Exp(a), the exponential distribution with failure rate 2. We showed in Sections 7.2 and 7.3 that â= 1/X is both the MME and the MLE of 2, and that its asymp- totic distribution is given by vn (Å - 1) PW~N (0,22) (8.53) Use the normal distribution in (8.53) to obtain, via a variance stabilizing transformation, an approximate 100(1 – a)% confidence interval for a.
4. Let X1, X2, ..., Xn be iid from the Bernoulli distribution with common probability mass function Px(x) = p*(1 – p)1-x for x = 0,1, and 0 < p < 1 14 a. (4) Find the MLE Ôule of p.
Again, let X1,..., Xn be iid observations from the Uniform(0,0) distribution. (a) Find the joint pdf of Xi) and X(n)- (b) Define R = X(n)-X(1) as the sample range. Find the pdf of R. (c) It turns out, if Xi, . . . , xn (iid) Uniform(0,0), E(R)-θ . What happens to E® as n increases? Briefly explain in words why this makes sense intuitively.
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