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Let p1,p2 denote the probability that a randomly selected male and female, respectively, has allergy to...

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Statistics

Let p1,p2 denote the probability that a randomly selected maleand female, respectively, has allergy to nuts. Let n1,n2 be thesample size of a random sample for male and female, respectively.Assume two samples are indepedent. Let X1,X2 be the number of maleand female who have allergy to nuts in the random sample,respectively.

(1) For parameters p1,p2, and p1−p2, find one unbiased estimatorfor each of them. And show why they are unbiased.

(2)Derive the formula for the standard error of those estimatorsin (1). Note that V(X−Y)=V(X)+V(Y) for two independent rv'sX,Y.

(3)For given samples, let n1=100,n2=150,x1=5,x2=9. Compute thethe value of those estimators in (1).

4) For given samples, let n1=100,n2=150,x1=5,x2=9. Compute theestimated standard errors of those estimators in (2)

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