(a) As sample variance S2 is an unbiased estimator of population variance o, the sample standard deviation S is an unbiased estimator of population standard deviation o. (b) If two independent populations (not necessarily normal) have equal variance o?, then pooled estimator S = m-1)Sf+(n-1)s is an unbiased estimator of o². (c) For a Bernoulli population, the population variance is maximum when p= 1/2. (d) Assuming we sample from a normal population, a (1- a)100% confidence interval for o? is given by (-1)s²_(n-1)S? The confidence interval width increases proportionally X-1,0/2 X-1,1-a/2 with n.
(a) As sample variance S2 is an unbiased estimator of population variance o, the sample standard deviation S is an unbiased estimator of population standard deviation o. (b) If two independent populations (not necessarily normal) have equal variance o?, then pooled estimator S = m-1)Sf+(n-1)s is an unbiased estimator of o². (c) For a Bernoulli population, the population variance is maximum when p= 1/2. (d) Assuming we sample from a normal population, a (1- a)100% confidence interval for o? is given by (-1)s²_(n-1)S? The confidence interval width increases proportionally X-1,0/2 X-1,1-a/2 with n.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Multiple choices.Which are corre
Transcribed Image Text:(a) As sample variance S is an unbiased estimator of population variance o², the sample
standard deviation S is an unbiased estimator of population standard deviation o.
(b) If two independent populations (not necessarily normal) have equal variance o?, then
pooled estimator S = (m-1S(-1)Si is an unbiased estimator of o?.
(c) For a Bernoulli population, the population variance is maximum when p = 1/2.
(d) Assuming we sample from a normal population, a (1- a)100% confidence interval for o?
(n-1)s2 (n-1)s
-1,0/2 X-1,1-a/2,
is given by
The confidence interval width increases proportionally
with n.
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