Question

(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.

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, · · · , yn be a random sample of size n from a...
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 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
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 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, . . ., 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...
. 2. Let Y1,Y2,...,Yn be i.i.d. draws from a distribution of mean µ. A test of...
. 2. Let Y1,Y2,...,Yn be i.i.d. draws from a distribution of mean µ. A test of H0 : µ ≥ 5 versus H1 : µ < 5 using the usual t-statistic yields a p-value of 0.03. a. Can we reject the null at 5% significance level (or α = 0.05)? Explain? b. How about at 1% significance level (or α = 0.01)? Explain? [Draw a figure to explain, if helpful.]
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.
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 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 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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT