(a) Discuss the two expressions 2(x₁ - x)² and (-1) 2(x,-)², both of which are used to measure the spread of a set of observations x₁, x2,. ..9 (b) A random sample of n observations is taken from a distribution; the sum of the observations is t₁, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on t₁ and ₂) for estimates of the mean and variance of the mean of a further, independent, random sample of size m, from the original distribution.
(a) Discuss the two expressions 2(x₁ - x)² and (-1) 2(x,-)², both of which are used to measure the spread of a set of observations x₁, x2,. ..9 (b) A random sample of n observations is taken from a distribution; the sum of the observations is t₁, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on t₁ and ₂) for estimates of the mean and variance of the mean of a further, independent, random sample of size m, from the original distribution.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![(6
(a) Discuss the two expressions
(x,-)² and
(x; — ѯ )² and (n − 1)²(x; -
-2(x,- 7 )², both of which are used
ni=1
to measure the spread of a set of observations x₁, X2,
Xn
.
(b) A random sample of n observations is taken from a distribution; the sum of the
observations is t₁, and the sum of the squares of the observations is 12. Explain how to estimate
the mean and the variance of the distribution from which the random sample was taken.
(c) Given the random sample described in part (b), write down expressions (based on 1₁
and ₂) for estimates of the mean and variance of the mean of a further, independent, random
sample of size m, from the original distribution.
(d) Given that n = 25, 1₁ = 400 and 1₂ = 8800, construct a 99% confidence interval for the
mean of the distribution, and use it to test whether or not this mean could be 20.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cb90dcb-f2a8-4448-a016-fccc3a5a7441%2F55d5810f-93dc-4c6f-b239-2a9148aac64a%2Ffkl25ye_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(6
(a) Discuss the two expressions
(x,-)² and
(x; — ѯ )² and (n − 1)²(x; -
-2(x,- 7 )², both of which are used
ni=1
to measure the spread of a set of observations x₁, X2,
Xn
.
(b) A random sample of n observations is taken from a distribution; the sum of the
observations is t₁, and the sum of the squares of the observations is 12. Explain how to estimate
the mean and the variance of the distribution from which the random sample was taken.
(c) Given the random sample described in part (b), write down expressions (based on 1₁
and ₂) for estimates of the mean and variance of the mean of a further, independent, random
sample of size m, from the original distribution.
(d) Given that n = 25, 1₁ = 400 and 1₂ = 8800, construct a 99% confidence interval for the
mean of the distribution, and use it to test whether or not this mean could be 20.
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