pulation, i.e. {Xifi=1• In al to pi. Please demonst

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Suppose we wish to estimate the expectation of a random variable X with a large popula-
tion. We observe n members of the population, i.e. {x;}1. Individual i is included in the
sample with a probability proportional to p;. Please demonstrate that the usual sample
E; ®i/Pi
i=1•
mean ī = n-1E, xi is no longer a consistent estimator for E[X], but ã
is.
E; 1/Pj
vi=1
Transcribed Image Text:Suppose we wish to estimate the expectation of a random variable X with a large popula- tion. We observe n members of the population, i.e. {x;}1. Individual i is included in the sample with a probability proportional to p;. Please demonstrate that the usual sample E; ®i/Pi i=1• mean ī = n-1E, xi is no longer a consistent estimator for E[X], but ã is. E; 1/Pj vi=1
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