In this task, a couple of sentences are sufficient for each point. (a) Briefly explain the difference between the following concepts. i. Unbiased Estimator and Biased Estimator ii. Population mean and sample mean (b) Briefly explain the following concepts. i. Random sample ii. Central limit theorem
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a) Briefly describe the two conditions that are sufficient to establish that an estimator is consistent. b) Briefly describe what we mean by an unbiased estimator. What are the key factors that determine the unbiasedness of an estimator? c) Are all unbiased estimators consistent? Please explain your answer [simple yes or no answer will not get any mark] d) Briefly describe how you would compare estimators that are not necessarily unbiased? e) Briefly describe one way of reducing sampling variance of an estimator.
Sri K.
(a) Give the definition of an unbiased estimator. (b) Explain what is meant by "the significance level of a test". (c) Explain what is meant by "the power of a test". (d) Name two methods of obtaining point estimators. (e) Name three methods of testing whether a sample comes from a normal distribution. (f) Complete the following statements in your answer book (i.e. give the missing words/expressions and do not waste time to rewrite everything). (i) Let X1, X2, ..., Xn be independent n (μ; σ^2) variates, each with probability density function fX (x) = 1/(σ√(2π)) e^(-1/2(x-μ)^2/σ^2), then X̄ = ∑(i=1 to n) Xi/n is a .................................. variate. (ii) The least squares estimators of θ1, θ2, ..., θk are found by .................................. Q (θ1, θ2, ..., θk) = ∑(i=1 to n) (Xi - E (Xi))^2. (iii) A type I error is committed if .................................. (iv) The power of a test is defined as P (..................................) (v) One-way analysis of variance is the problem of comparing the sample .................................. of more than two independent samples.
Madhur L.
Briefly define each of the following: a. Distribution of sample means b. Central limit theorem c. Expected value of $M$ d. Standard error of $M$
Joanna Q.
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