Question

Suppose data collected suggest a Bernoulli distribution with parameter θ (a special case of the binomial...

Suppose data collected suggest a Bernoulli distribution with parameter θ (a special case of the binomial distribution).

a) Use the method of moments to obtain an estimator of θ.

b) Obtain the maximum likelihood estimator (MLE) of θ.

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
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...
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 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...
suppose we draw a random sample of size n from a Poisson distribution with parameter λ....
suppose we draw a random sample of size n from a Poisson distribution with parameter λ. show that the maximum likelihood estimator for λ is an efficient estimator
Let X1,X2,...,Xn be i.i.d. Geometric(θ), θ = 1,2,3,... random variables. a) Find the maximum likelihood estimator...
Let X1,X2,...,Xn be i.i.d. Geometric(θ), θ = 1,2,3,... random variables. a) Find the maximum likelihood estimator of θ. b) In a certain hard video game, a player is confronted with a series of AI opponents and has an θ probability of defeating each one. Success with any opponent is independent of previous encounters. Until first win, the player continues to AI contest opponents. Let X denote the number of opponents contested until the player’s first win. Suppose that data of...
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...
#1 A sample of 4 observations (X1 = 0.4, X2 = 0.6, X3 = 0.7, X4...
#1 A sample of 4 observations (X1 = 0.4, X2 = 0.6, X3 = 0.7, X4 = 0.9) is collected from a continuous distribution with pdf (a) Find the point estimate of θ by the Method of Moments. (b) Find the point estimate of θ by the Method of Maximum Likelihood. Use two decimal places.
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
use R software Suppose that X1, …, Xn are a random sample from a lognormal distribution....
use R software Suppose that X1, …, Xn are a random sample from a lognormal distribution. Construct a 95% confidence interval for the parameter μ. Use a Monte Carlo method to obtain an empirical estimate of the confidence level when data is generated from standard lognormal.
The shear strength of each of ten test spot welds is determined, yielding the following data...
The shear strength of each of ten test spot welds is determined, yielding the following data (psi). 367 415 391 409 362 389 396 382 375 358 (a) Assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of maximum likelihood. (Round your answers to two decimal places.) average psi? standard deviation psi? (b) Again assuming a normal distribution, estimate the strength value below which 95% of all...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT