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When S successes occur in n trials, the sample proportion p ˆ =S/n is customarily used...

When S successes occur in n trials, the sample proportion p ˆ =S/n is customarily used as an estimator of the probability of success p. However, sometimes there are good reasons to use the estimator ˆ p* =(S+1)/ n+2

a) Find the MSE (Mean Squared Error) of p ˆ (phat). [5 marks]

b) Find the bias of ˆ p* (phat*). What is the value of the bias if p=0.4? [5 marks]

c) Suppose that it is known that p is close to 0.4 and n=1,000. Which estimator would you prefer?

Math   Statistics-And-Probability   
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