X is a statistic and an estimator of the parameter__and s is a statistic and an estimator of the parameter
Answer:
Given that:
is a statistic and an estimator of the parameter and is a statistic and an estimator of the parameter
i.e
Option (a) is correct answer
X is a statistic and an estimator of the parameter__and s is a statistic and an estimator of the parameter
2. Suppose § is an unbiased OLS estimator of parameter B, and the t-statistic t = 878~t(m), where m is the degrees of freedom. How to construct a 95% interval estimator of B? How to interpret this interval estimator?
Please answer all parts. 7. A sample statistic is an estimator of the population parameter, if the mean of the sampling distribution for the sample statistic is the 8. A distribution has a mean of 12 and a variance of 250. Find the second moment about the origin. Answer:
Complete the sentence: An unbiased estimator is _____. a. any sample statistic used to approximate a population parameter b. a sample statistic, which has an expected value equal to the value of the population parameter c. a sample statistic whose value is usually less than the value of the population parameter d. any estimator whose standard error is relatively small
44 Let X,..., X. be a random sample from Find the Pitman estimator for the location parameter (f) Using the prior density g(0)--e-n,”(θ. find the posterior Bayes estimator (g) Of θ. 44 Let X,..., X. be a random sample from Find the Pitman estimator for the location parameter (f) Using the prior density g(0)--e-n,”(θ. find the posterior Bayes estimator (g) Of θ.
Letter f and g only. 44 Let X,..., X. be a random sample from (a) Find a sufficient statistic. (b) Find a maximum-likelihood estimator of θ. (c) Find a method-of-moments estimator of θ. (d) Is there a complete sufficient statistic? If so, find it. (e) Find the UMVUE of 0 if one exists. (f) Find the Pitman estimator for the location parameter θ. (g) Using the prior density g(0)--e-n,๑)(8), find the posterior Bayes estimator Of θ. 44 Let X,..., X....
QUESTION 7 The sample statistic s is the point estimator of а. х b.u с. о Od.p
7. Let X1,....Xn random sample from a Bernoulli distribution with parameter p. A random variable X with Bernoulli distribution has a probability mass function (pmf) of with E(X) = p and Var(X) = p(1-p). (a) Find the method of moments (MOM) estimator of p. (b) Find a sufficient statistic for p. (Hint: Be careful when you write the joint pmf. Don't forget to sum the whole power of each term, that is, for the second term you will have (1...
2. (a) Define the bias of ˆ θ as an estimator for the parameter θ. [2 marks] (b) For independent random variables X1,X2,...,Xn, assume that E(Xi) = µ and var(Xi) = σ2, i = 1,...,n. (i) Show that ˆ µ1 = {(X1+Xn)/2}is an unbiased estimator for µ and determine its variance. [3 marks] (ii) Find the relative efficiency of ˆ µ1 to the unbiased estimator ˆ µ2 = X, the sample mean. [2 marks] (iii) Is ˆ µ1 a consistent...
distribution with shape parameter 3 and unknown scale parameter, λ. Thus the density of Xis given by: a) Find a sufficient statistic for λ is the statistic minimal sufficient? b) Find the MLE for and verify that it is a function of the statistic in a) c) Find it) and hence give the CRLB for an unbiased estimator of λ d) Find the distribution of the sufficient statistic in (a) distribution with shape parameter 3 and unknown scale parameter, λ....
4. Find the maximuln likelihood estimator of the parameter θ of the population with the density Extra: Is the maximum likelihood estimator found in Problem 4 unbiased?