Question

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 of the double exponential distribution.

e) Find the method of moments estimator of θ.

f) Show the maximum likelihood estimator is a MVUE of θ.

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

Homework Answers

Answer #1

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 of an exponential population with parameter θ....
Let Y1, Y2, ... Yn be a random sample of an exponential population with parameter θ. Find the density function of the minimum of the sample Y(1) = min⁡(Y1, Y2, ..., Yn).
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.
Suppose Y1,··· ,Yn is a sample from a exponential distribution with mean θ, and let Y(1),···...
Suppose Y1,··· ,Yn is a sample from a exponential distribution with mean θ, and let Y(1),··· ,Y(n) denote the order statistics of the sample. (a) Find the constant c so that cY(1) is an unbiased estimator of θ. (b) Find the sufficient statistic for θ and MVUE for θ.
Let Y1,Y2,...,Yn denote a random sample of size n from a population with a uniform distribution...
Let Y1,Y2,...,Yn denote a random sample of size n from a population with a uniform distribution on the interval (0,θ). Let Y(n)= max(Y1,Y2,...,Yn) and U = (1/θ)Y(n) . a) Show that U has cumulative density function 0 ,u<0, Fu (u) =   un ,0≤u≤1, 1 ,u>1
1. (a) Y1,Y2,...,Yn form a random sample from a probability distribution with cumulative distribution function FY...
1. (a) Y1,Y2,...,Yn form a random sample from a probability distribution with cumulative distribution function FY (y) and probability density function fY (y). Let Y(1) = min{Y1,Y2,...,Yn}. Write the cumulative distribution function for Y(1) in terms of FY (y) and hence show that the probability density function for Y(1) is fY(1)(y) = n{1−FY (y)}n−1fY (y). [8 marks] (b) An engineering system consists of 5 components connected in series, so, if one components fails, the system fails. The lifetimes (measured in...
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.
Let Y1, Y2, . . . , Yn denote a random sample from a uniform distribution...
Let Y1, Y2, . . . , Yn denote a random sample from a uniform distribution on the interval (0, θ). (a) (5 points)Find the MOM for θ. (b) (5 points)Find the MLE 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.
Let Y1, Y2, Y3 ,..,, Yn be a random sample from a normal distribution with mean...
Let Y1, Y2, Y3 ,..,, Yn be a random sample from a normal distribution with mean µ and standard deviation 1. Then find the MVUE( Minimum - Variance Unbiased Estimation) for the parameters: µ^2 and µ(µ+1)
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?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT