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Asked Nov 16, 2019
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List two unbiased estimators and their corresponding parameters. 

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Expert Answer

Step 1

Unbiased estimators:

An estimator is used to study the population whose parameters are unknown. An estimator acts as proxy to represent the parameters of population. The estimate that has been can be either biased or unbiased which is completely depend the population parameter described.

Step 2

1.

Here, X1, X2, …, Xn be a random sample of size n taken from the given exponential distribution with parameter.

For a random variable, Xi having the given exponential distribution, E (Xi) = τ.

The MLE of the exponential parameter τ is unbiased estimator of the the sample mean.

The proof of MLE is unbiased is given below:

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MLE, X E() E(X) - ,Σ MLE is unbiased.

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Step 3

2.

If Xi is a Bernoulli random variable with parameter p, then E(Xi)=p. Prove that the maximum likelihood e...

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η E(β) =Ε Σx η 1 ΣΕΧ) 72 η Σ. 77 - 1φ) (пр) 77 = p

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