Question

Let X1,X2, . . . ,Xn be a random sample of size n from a geometric...

Let X1,X2, . . . ,Xn be a random sample of size n
from a geometric distribution for which p is the probability
of success.
(a) Find the maximum likelihood estimator of p (don't use method of moment).
(b) Explain intuitively why your estimate makes good
sense.
(c) Use the following data to give a point estimate of p:
3 34 7 4 19 2 1 19 43 2
22 4 19 11 7 1 2 21 15 16

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
Probability and Statistical Inference (10th Edition) Chapter 6: Point Estimation; Section 6.4: Maximum Likelihood and Moment...
Probability and Statistical Inference (10th Edition) Chapter 6: Point Estimation; Section 6.4: Maximum Likelihood and Moment of Methods Estimation Exercise 6.4-10 6.4-10. Let X1,X2,...,Xn be a random sample of size n from a geometric distribution for which p is the probability of success. (a) Use the method of moments to find a point estimate for p. (b) Explain intuitively why your estimate makes good sense. (c) Use the following data to give a point estimate of p: 3, 34, 7,...
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
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.
1. Let X1, X2, . . . , Xn be a random sample from a distribution...
1. Let X1, X2, . . . , Xn be a random sample from a distribution with pdf f(x, θ) = 1 3θ 4 x 3 e −x/θ , where 0 < x < ∞ and 0 < θ < ∞. Find the maximum likelihood estimator of ˆθ.
Let X1,X2,...,Xn be a random sample from a geometric random variable with parameter p. What is...
Let X1,X2,...,Xn be a random sample from a geometric random variable with parameter p. What is the density function ofU = min({X1,X2,...,Xn})
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 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
6. Let θ > 1 and let X1, X2, ..., Xn be a random sample from...
6. Let θ > 1 and let X1, X2, ..., Xn be a random sample from the distribution with probability density function f(x; θ) = 1/(xlnθ) , 1 < x < θ. a) Obtain the maximum likelihood estimator of θ, ˆθ. b) Is ˆθ a consistent estimator of θ? Justify your answer.
Let X1, X2, . . . , Xn be iid exponential random variables with unknown mean...
Let X1, X2, . . . , Xn be iid exponential random variables with unknown mean β. (1) Find the maximum likelihood estimator of β. (2) Determine whether the maximum likelihood estimator is unbiased for β. (3) Find the mean squared error of the maximum likelihood estimator of β. (4) Find the Cramer-Rao lower bound for the variances of unbiased estimators of β. (5) What is the UMVUE (uniformly minimum variance unbiased estimator) of β? What is your reason? (6)...
Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ). Let Yn...
Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ). Let Yn be the maximum of X1, X2, ..., Xn. (a) Give the pdf of Yn. (b) Find the mean of Yn. (c) One estimator of θ that has been proposed is Yn. You may note from your answer to part (b) that Yn is a biased estimator of θ. However, cYn is unbiased for some constant c. Determine c. (d) Find the variance of cYn,...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT