The following estimators for the defect rate

*p*are proposed:

A) What is the distribution of X1 and X2, and what expectation and variance do they have?

X1 og X2 follows a binomial distribution.

Expected value: E(X1 + X2) = E(X1) + E(X2) = 30p + 70p = 100p

Variance:

Var(X1 + X2) = Var(X1) + Var(X2) = 30p(1-p) + 70p(1-p) = 100p(1-p)

b) Find the expectation of each of the estimators. Which of them is unbiased?

All look like equally unbiased

c) Find the variance of each of the estimators. Which is best? Try to explain why this one the estimator is better than the others.

The first estimator is best, because it has the lowest variance.

d) Why can the estimators p3 and p4 be less robust than the first two estimators?

How would you interpret it if the two estimators p3 and p4 give very different results?