3.1. In another form of sum quota sampling (see V, Section 4.2), a sequence of nonnegative independent and identically distributed random variables X XZ, ... is observed, the sampling continuing until the first time that the sum of the observations exceeds the quota t. In renewal process terminology, the sample size is N(t) + 1. The sample mean is

An important question in statistical theory is whether or not this sample mean is unbiased. That is, how does the expected value of this sample

Hint: Use the result of the previous exercise, that WN(,)+, and N(t)
are independent, and then evaluate separately

Transcribed Image Text:

WN(D)+1 N(t) +1 N(r)+1 N(t) + 1