7.(3pts)Suppose you are interested in estimating the mean of a population of valuesμfrom a random sample of size 3.The variance of the population isσ2.Select the statement that best describes which estimator would you prefer. AssumeX1, X2andX3are iid random variables from the population. Would you prefer to use ˆμ1or ˆμ2?ˆμ1= 2X1-X2ˆμ2=X1+X2-X3?
8.(4 pts)Identify whether the random variable X in each of the following scenerios is a binomial random variable or not. Ifnot, in a few words explain what assumption[s] is[/are] not well met.(I) According to a recent study, 63% of children wear their bike helmets always, 24% wear them often, and 13% hardlyever wear them. If you interview 15 children, let X be the number that report hardly ever wearing a helmet.(II) You have a bag of 10 batteries, in which 2 are defective. Suppose you put 4 batteries into your calculator from thebag. Let X be the number of defective batteries in your calculator.