Question

Let X1,...,Xn be a random sample from the pdf f(x;θ) = θx^(θ−1) , 0 ≤ x...

Let X1,...,Xn be a random sample from the pdf f(x;θ) = θx^(θ−1) , 0 ≤ x ≤ 1 , 0 < θ < ∞ Find the method of moments estimator of θ.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Given pdf:

                            0 x1

                            0 < <

between the limits 0 to 1.

Applying limts, we ge:

So, we can stimate with:

So,

The method of moments estimator of is given by:

,

where is the sample mean given by:

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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, ..., Xn} be i.i.d. from a distribution with pdf f(x; θ) = θ/xθ+1 for...
Let {X1, ..., Xn} be i.i.d. from a distribution with pdf f(x; θ) = θ/xθ+1 for θ > 2 and x > 1. (a) (10 points) Calculate EX1 and V ar(X1). (b) (5 points) Find the method of moments estimator of θ. (c) (5 points) If we denote the method of moments estimator as ˆθ1. What does √ n( ˆθ1 − θ) converge in distribution to? (d) (5 points) Is the method of moment estimator efficient? Verify your answer.
Let X1, . . . , Xn be a random sample from the following pdf: f(x|θ)=...
Let X1, . . . , Xn be a random sample from the following pdf: f(x|θ)= (x/θ)*e^(-x^2/2θ). x>0 (a) Find a sufficient statistic for θ.
Consider a random sample X1, X2, ⋯ Xn from the pdf fx;θ=.51+θx, -1≤x≤1;0, o.w., where (this...
Consider a random sample X1, X2, ⋯ Xn from the pdf fx;θ=.51+θx, -1≤x≤1;0, o.w., where (this distribution arises in particle physics). Find the method of moment estimator of θ. Compute the variance of your estimator. Hint: Compute the variance of X and then apply the formula for X, etc.
Let X1,..., Xn be a random sample from a distribution with pdf as follows: fX(x) =...
Let X1,..., Xn be a random sample from a distribution with pdf as follows: fX(x) = e^-(x-θ) , x > θ 0 otherwise. Find the sufficient statistic for θ. Find the maximum likelihood estimator of θ. Find the MVUE of θ,θˆ Is θˆ a consistent estimator of θ?
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
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.
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...
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
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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT