Question

Suppose X1 ...... Xn is a random sample from the uniform distribution on [a; b]. (a)...

Suppose X1 ...... Xn is a random sample from the uniform distribution on [a; b].

(a) Find the method of moments estimators of a and b.

(b) Find the maximum likelihood estimators of a and b.

please step by step

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 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.)
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.
Let X1, X2, . . . Xn be iid random variables from a gamma distribution with...
Let X1, X2, . . . Xn be iid random variables from a gamma distribution with unknown α and unknown β. Find the method of moments estimators for α and β
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.
Let X2, ... , Xn denote a random sample from a discrete uniform distribution over the...
Let X2, ... , Xn denote a random sample from a discrete uniform distribution over the integers - θ, - θ + 1, ... , -1, 0, 1, ... ,  θ - 1,  θ, where  θ is a positive integer. What is the maximum likelihood estimator of  θ? A) min[X1, .. , Xn] B) max[X1, .. , Xn] C) -min[X1, .. , Xn​​​​​​​] D) (max[X1, .. , Xn​​​​​​​] - min[X1, .. , Xn​​​​​​​]) / 2 E) max[|X1| , ... , |Xn|]
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
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 Bernoulli distribution. Under the condition...
Let X1, X2, ·······, Xn be a random sample from the Bernoulli distribution. Under the condition 1/2≤Θ≤1, find a maximum-likelihood estimator of Θ.
Let B > 0 and let X1 , X2 , … , Xn be a random...
Let B > 0 and let X1 , X2 , … , Xn be a random sample from the distribution with probability density function. f( x ; B ) = β/ (1 +x)^ (B+1), x > 0, zero otherwise. (i) Obtain the maximum likelihood estimator for B, β ˆ . (ii) Suppose n = 5, and x 1 = 0.3, x 2 = 0.4, x 3 = 1.0, x 4 = 2.0, x 5 = 4.0. Obtain the maximum likelihood...
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
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT