Question

Determine the form of a minimal sufficient statistic for a sample of size n from the...

Determine the form of a minimal sufficient statistic for a sample of size n from the Uniform[0,θ] model where θ> 0

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
Suppose that (X1, · · · , Xn) is a random sample from uniform distribution U(0,...
Suppose that (X1, · · · , Xn) is a random sample from uniform distribution U(0, θ). (a) Prove that T(X1, · · · , Xn) = X(n) is minimal sufficient for θ. (X(n) is the largest order statistic, i.e., X(n) = max{X1, · · · , Xn}.) (b) In addition, we assume θ ≥ 1. Find a minimal sufficient statistic for θ and justify your answer.
Show that the sum of the observations of a random sample of size n from a...
Show that the sum of the observations of a random sample of size n from a gamma distribution that has pdf f(x; θ) = (1/θ)e^(−x/θ), 0 < x < ∞, 0 < θ < ∞, zero elsewhere, is a sufficient statistic for θ. Use Neyman's Factorization Theorem.
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.
Suppose a random sample of size n is drawn from the pdf f(sub)Y(y;θ) =1/θ, 0 ≤...
Suppose a random sample of size n is drawn from the pdf f(sub)Y(y;θ) =1/θ, 0 ≤ y ≤ θ. Find a 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 that X1,..., Xn form a random sample from the uniform distribution on the interval [0,θ],...
Suppose that X1,..., Xn form a random sample from the uniform distribution on the interval [0,θ], where the value of the parameter θ is unknown (θ>0). (1)What is the maximum likelihood estimator of θ? (2)Is this estimator unbiased? (Indeed, show that it underestimates the parameter.)
Let X be the mean of a random sample of size n from a N(θ, σ2)...
Let X be the mean of a random sample of size n from a N(θ, σ2) distribution, −∞ < θ < ∞, σ2 > 0. Assume that σ2 is known. Show that X 2 − σ2 n is an unbiased estimator of θ2 and find its efficiency.
Let X1, X2,...,Xn be a random sample from Bernoulli (p). Determine a sufficient statistic for p...
Let X1, X2,...,Xn be a random sample from Bernoulli (p). Determine a sufficient statistic for p and derive the UMVUE and MLE of T(p)=p^2(1-p)^2.
a. If ? ̅1 is the mean of a random sample of size n from a...
a. If ? ̅1 is the mean of a random sample of size n from a normal population with mean ? and variance ?1 2 and ? ̅2 is the mean of a random sample of size n from a normal population with mean ? and variance ?2 2, and the two samples are independent, show that ?? ̅1 + (1 − ?)? ̅2 where 0 ≤ ? ≤ 1 is an unbiased estimator of ?. b. Find the value...
Suppose that X1,...,Xn ∼ U(0,θ); that is, a sample of N observations from a random variable...
Suppose that X1,...,Xn ∼ U(0,θ); that is, a sample of N observations from a random variable with a uniform distribution where the lower bound is 0 and the upper bound θ is unknown. Find the maximum likelihood estimate of θ, also demonstrating this in R. Draw the pdf and the likelihood, and explain what they represent, in R.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT