A coin is assumed to be unfair with P(head) = p where p is unknown. To estimate p, you can toss acoin n times independently and observe the number of heads shown. Let X be the number of headsshown in n tosses.(a) Is p₁ = X/n an unbiased estimator for p? Show your work.(b) Is P2 = X²/n an unbiased estimator for p? Show your work.(c) Is P3 = (X+1)/(n+2) an unbiased estimator for p? Show your work.(d) Consider the following results of 10 tosses of a coin:H, T, T, T, T, H, T, H, T, TEstimate the probability of head for this coin by using P1, P2, and P3. If you have to select oneof them, which estimate do you choose? Why?(e) Estimate the standard error of your chosen estimate in part (d).

As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

Answered: A coin is assumed to be unfair with…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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