Question

In: Statistics and Probability

Let X1, X2,....,Xn be i.i.d P(theta) a) find the UMP test H0:theta=theta0 v.s H1 :theta>theta0 b)...

Let X1, X2,....,Xn be i.i.d P(theta)

a) find the UMP test H0:theta=theta0 v.s H1 :theta>theta0

b) sketch the power function for theta0=1 ^ n=30 use alpha =0.05

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Let X1, . . . , Xn ∼ iid Beta(θ, 1). (a) Find the UMP test...
Let X1, . . . , Xn ∼ iid Beta(θ, 1). (a) Find the UMP test for H0 : θ ≥ θ0 vs H1 : θ < θ0. (b) Find the corresponding Wald test. (c) How do these tests compare and which would you prefer?
6. Let X1; : : : ;Xn be i.i.d. samples from Uniform(0;theta ). (a) Find cn...
6. Let X1; : : : ;Xn be i.i.d. samples from Uniform(0;theta ). (a) Find cn such that Theta1 = cn min(X1; : : : ;Xn) is an unbiased estimator of theta (b) It is easy to show that theta2 = 2(X-bar) is also an unbiased estimator of theta(you do not need to show this). Compare theta1 and theta2. Which is a better estimator of theta? Specify your criteria.
Let X1, X2, · · · , Xn (n ≥ 30) be i.i.d observations from N(µ1,...
Let X1, X2, · · · , Xn (n ≥ 30) be i.i.d observations from N(µ1, σ12 ) and Y1, Y2, · · · , Yn be i.i.d observations from N(µ2, σ22 ). Also assume that X's and Y's are independent. Suppose that µ1, µ2, σ12 , σ22  are unknown. Find an approximate 95% confidence interval for µ1µ2.
For a fixed θ>0, let X1,X2,…,Xn be i.i.d., each with the beta (1,θ) density. i) Find...
For a fixed θ>0, let X1,X2,…,Xn be i.i.d., each with the beta (1,θ) density. i) Find θ^ that is the maximum likelihood estimate of θ. ii) Let X have the beta (1,θ) density. Find the density of −log⁡(1−X). Recognize this as one of the famous ones and provide its name and parameters. iii) Find f that is the density of the MLE θ^ in part (i).
Let X1, . . . , Xn ∼ iid Exp(θ) and consider the test for H0...
Let X1, . . . , Xn ∼ iid Exp(θ) and consider the test for H0 : θ ≥ θ0 vs H1 : θ < θ0. (a) Find the size-α LRT. Express the rejection region in the form of R = {X > c ¯ } where c will depend on a value from the χ 2 2n distribution. (b) Find the appropriate value of c. (c) Find the formula for the P-value of this test. (d) Compare this test...
Let X1,..., Xn be an i.i.d. sample from a geometric distribution with parameter p. U =...
Let X1,..., Xn be an i.i.d. sample from a geometric distribution with parameter p. U = ( 1, if X1 = 1, 0, if X1 > 1) find a sufficient statistic T for p. find E(U|T)
Let X1,X2,...,Xn be i.i.d. Gamma random variables with parameters α and λ. The likelihood function is...
Let X1,X2,...,Xn be i.i.d. Gamma random variables with parameters α and λ. The likelihood function is difficult to differentiate because of the gamma function. Rather than finding the maximum likelihood estimators, what are the method of moments estimators of both parameters α and λ?
Let X1, X2, ..., Xn be a random sample from Exp(?). Find the MVUE of the...
Let X1, X2, ..., Xn be a random sample from Exp(?). Find the MVUE of the median of this exponential distribution.
Let X = ( X1, X2, X3, ,,,, Xn ) is iid, f(x, a, b) =...
Let X = ( X1, X2, X3, ,,,, Xn ) is iid, f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b < 1 then, find a two dimensional sufficient statistic for (a, b)
Let X1,...,Xn be i.i.d. N(θ,1), where θ ∈ R is the unknown parameter. (a) Find an...
Let X1,...,Xn be i.i.d. N(θ,1), where θ ∈ R is the unknown parameter. (a) Find an unbiased estimator of θ^2 based on (Xn)^2. (b) Calculate it’s variance and compare it with the Cram ́er-Rao lower bound.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT