Question

In a pasta factory, due to a miscalibration of the machinery, all spaghetti sticks produced had different lengths on a given day, then randomly packed & shipped to different locations and consumers. We wonder the length of the longest spaghetti stick produced that day. Offer a good statistical estimator to address this problem and discuss/evaluate its properties.

Answer 1

suppose we collect n sample

X1,X2 ,...,Xn

X(n) = max(X1,X2,...,Xn)

X(n) is good estimator for longest spaghetti stick produced that day

This is biased

this is consistent