Question

5. Let Y1, Y2, ...Yn (independent and identically distributed. ∼ f(y; α) = 1/6 α8y3 ·...

5. Let Y1, Y2, ...Yn (independent and identically distributed. ∼ f(y; α) = 1/6 α8y3 · e^(−α2y3 ), 0 ≤ y < ∞, 0 < α < ∞.

(a) (8 points) Find an expression for the Method of Moments estimator of α, ˜α. Show all work.

(b) (8 points) Find an expression for the Maximum Likelihood estimator for α, ˆα. Show all work.

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

Homework Answers

Answer #1

Dear please Thumbs Up.....

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 Y1, Y2, . . ., Yn be a random sample from a Laplace distribution with...
Let Y1, Y2, . . ., Yn be a random sample from a Laplace distribution with density function f(y|θ) = (1/2θ)e-|y|/θ for -∞ < y < ∞ where θ > 0. The first two moments of the distribution are E(Y) = 0 and E(Y2) = 2θ2. a) Find the likelihood function of the sample. b) What is a sufficient statistic for θ? c) Find the maximum likelihood estimator of θ. d) Find the maximum likelihood estimator of the standard deviation...
Let Y1, Y2, . . . , Yn be independent and identically distributed Beta(θ, 1), θ...
Let Y1, Y2, . . . , Yn be independent and identically distributed Beta(θ, 1), θ > 0. (a) Find the MOM estimator for θ. (b) Find the ML estimator θˆ of θ. (c) Find the ML estimator τˆ of τ = P(Y1 ≤ a), for a ∈ (0,1). (d) Find a function of the ML estimator that is a pivotal quantity and use it to construct a two-sided 1−α CI for θ.
Let Y1,Y2.....,Yn be independent ,uniformly distributed random variables on the interval[0,θ].，Y(n)=max(Y1,Y2,....,Yn)，which is considered as an estimator...
Let Y1,Y2.....,Yn be independent ,uniformly distributed random variables on the interval[0,θ].，Y(n)=max(Y1,Y2,....,Yn)，which is considered as an estimator of θ. Explain why Y is a good estimator for θ when sample size is large.
Problem 3. Let Y1, Y2, and Y3 be independent, identically distributed random variables from a population...
Problem 3. Let Y1, Y2, and Y3 be independent, identically distributed random variables from a population with mean µ = 12 and variance σ 2 = 192. Let Y¯ = 1/3 (Y1 + Y2 + Y3) denote the average of these three random variables. A. What is the expected value of Y¯, i.e., E(Y¯ ) =? Is Y¯ an unbiased estimator of µ? B. What is the variance of Y¯, i.e, V ar(Y¯ ) =? C. Consider a different estimator...
Suppose Y1, . . . , Yn are independent random variables with common density fY(y) =...
Suppose Y1, . . . , Yn are independent random variables with common density fY(y) = eμ−y , y > μ 1. Find the Method of Moments Estimator for μ. 2. Find the MLE for μ. Then find the bias of the estimator
Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on...
Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on the interval (θ - λ, θ + λ) where -∞ < θ < ∞ and λ > 0. Find the method of moments estimators of θ and λ.
(a) Let Y1,Y2,··· ,Yn be i.i.d. with geometric distribution P(Y = y) = p(1−p)y-1 y=1, 2,...
(a) Let Y1,Y2,··· ,Yn be i.i.d. with geometric distribution P(Y = y) = p(1−p)y-1 y=1, 2, ........, 0<p<1. Find a sufficient statistic for p. (b) Let Y1,··· ,yn be a random sample of size n from a beta distribution with parameters α = θ and β = 2. Find the sufficient statistic for θ.
Let y1,y2,...,yn denote a random sample from a Weibull distribution with parameters m=3 and unknown alpha:...
Let y1,y2,...,yn denote a random sample from a Weibull distribution with parameters m=3 and unknown alpha: f(y)=(3/alpha)*y^2*e^(-y^3/alpha) y>0 0 otherwise Find the MLE of alpha. Check when its a maximum
if 2 random variables have a joint density f(y1, y2) = 6/5. * (y1 + y2^2)...
if 2 random variables have a joint density f(y1, y2) = 6/5. * (y1 + y2^2) What is an expression for f(y1|y2) for 0<y2<1 and then for f(y1| y2 =0.25)? Find E(Y1| Y2 = 0.25)
[8] Let Y1<Y2<...<Yn be the order statistics of n independent observations from U(0, 1). (i) Find...
[8] Let Y1<Y2<...<Yn be the order statistics of n independent observations from U(0, 1). (i) Find the p.d.f. of the r-th order statistics Yr. (ii) Find the mean and variance of Yr.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT