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Please answer all parts of the problem, if possible. Let X ~ Binomial (1, p)  0 <p<1...

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Basic Math

Please answer all parts of the problem, if possible.

Let X ~ Binomial (1, p)  0

R 0 - different parameter values have different functions.

R 1 - parameter space does not contain its own endpoints.

R 2. - the set of points x where f (x, p) is not zero and shouldnot depend on p.

R 3. One derivative can be found with respect to p.

R 4. Two derivatives can be found with respect to p.

b. Find the maximum likelihood estimator of p, call it Yn forthis problem.

c. Is Yn unbiased? Explain.

d. Show that Yn is consistent asymptotically normal and identifythe asymptotic normal variance.

e. Variance-stabilize your result in (d) or show there is noneed to do so.

f. Compute I (p) where I is Fisher’s Information. g. Compute theefficiency of Yn for p (or show that you should not!).

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