Question

   When X1, X2, ..., and Xn are probability samples from a population whose probability density...

   When X1, X2, ..., and Xn are probability samples from a population whose probability density functions are f(x) = 3x^2 / θ^3, 0 < x < θ.
   a. Determine constant c so that cx̅ becomes the unbiased estimator of θ
b. Find 95% confidence interval of θ.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X1, X2, ..., Xn be a random sample from a distribution with probability density function...
Let X1, X2, ..., Xn be a random sample from a distribution with probability density function f(x; θ) = (θ 4/6)x 3 e −θx if 0 < x < ∞ and 0 otherwise where θ > 0 . a. Justify the claim that Y = X1 + X2 + ... + Xn is a complete sufficient statistic for θ. b. Compute E(1/Y ) and find the function of Y which is the unique minimum variance unbiased estimator of θ. b.  Compute...
A random sample X1, X2, . . . , Xn is drawn from a population with...
A random sample X1, X2, . . . , Xn is drawn from a population with pdf. f(x; β) = (3x^2)/(β^3) , 0 ≤ x ≤ β 0, otherwise (a) [6] Find the pdf of Yn, the nth order statistic of the sample. (b) [4] Find E[Yn]. (c) [4] Find Var[Yn]. (d)[3] Find the mean squared error of Yn when Yn is used as a point estimator for β (e) [2] Find an unbiased estimator for β.
Let X1, X2,..., Xn be a random sample from a population with probability density function f(x)...
Let X1, X2,..., Xn be a random sample from a population with probability density function f(x) = theta(1-x)^(theta-1), where 0<x<1, where theta is a positive unknown parameter a) Find the method of moments estimator of theta b) Find the maximum likelihood estimator of theta c) Show that the log likelihood function is maximized at theta(hat)
Let X1, X2, . . . , Xn be iid random variables with pdf f(x|θ) =...
Let X1, X2, . . . , Xn be iid random variables with pdf f(x|θ) = θx^(θ−1) , 0 < x < 1, θ > 0. Is there an unbiased estimator of some function γ(θ), whose variance attains the Cramer-Rao lower bound?
Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ). Let Yn...
Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ). Let Yn be the maximum of X1, X2, ..., Xn. (a) Give the pdf of Yn. (b) Find the mean of Yn. (c) One estimator of θ that has been proposed is Yn. You may note from your answer to part (b) that Yn is a biased estimator of θ. However, cYn is unbiased for some constant c. Determine c. (d) Find the variance of cYn,...
Let X1, X2 · · · , Xn be a random sample from the distribution with...
Let X1, X2 · · · , Xn be a random sample from the distribution with PDF, f(x) = (θ + 1)x^θ , 0 < x < 1, θ > −1. Find an estimator for θ using the maximum likelihood
6. Let θ > 1 and let X1, X2, ..., Xn be a random sample from...
6. Let θ > 1 and let X1, X2, ..., Xn be a random sample from the distribution with probability density function f(x; θ) = 1/(xlnθ) , 1 < x < θ. a) Obtain the maximum likelihood estimator of θ, ˆθ. b) Is ˆθ a consistent estimator of θ? Justify your answer.
1. Let X1, X2, . . . , Xn be a random sample from a distribution...
1. Let X1, X2, . . . , Xn be a random sample from a distribution with pdf f(x, θ) = 1 3θ 4 x 3 e −x/θ , where 0 < x < ∞ and 0 < θ < ∞. Find the maximum likelihood estimator of ˆθ.
Let X1, X2, · · · , Xn be a random sample from the distribution, f(x;...
Let X1, X2, · · · , Xn be a random sample from the distribution, f(x; θ) = (θ + 1)x^ −θ−2 , x > 1, θ > 0. Find the maximum likelihood estimator of θ based on a random sample of size n above
6. Let X1, X2, ..., Xn be a random sample of a random variable X from...
6. Let X1, X2, ..., Xn be a random sample of a random variable X from a distribution with density f (x)  ( 1)x 0 ≤ x ≤ 1 where θ > -1. Obtain, a) Method of Moments Estimator (MME) of parameter θ. b) Maximum Likelihood Estimator (MLE) of parameter θ. c) A random sample of size 5 yields data x1 = 0.92, x2 = 0.7, x3 = 0.65, x4 = 0.4 and x5 = 0.75. Compute ML Estimate...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT