pulation, i.e. {Xifi=1• In al to pi. Please demonst
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33f6b54a-6f69-413c-bec3-3cce8812b9e5%2Fef0e599c-d272-4c66-a8fa-1471a83b5a80%2F1twhr6o_processed.jpeg&w=3840&q=75)
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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