76. Let ī, and s denote the sample mean and variancefor the sample x1, ... , X, and let īp+1 and sdenote these quantities when an additional obser-vation x41 is added to the sample.a. Show how xp+1 can be computed from x, and'n+1Xn+1.b. Show thatns= (n – 1)s, +-- (xn+1 – Xn)²n+1so that s can be computed from x,„41, Xn,and s?.'n+1c. Suppose that a sample of 15 strands of draperyyarn has resulted in a sample mean threadelongation of 12.58 mm and a sample standarddeviation of .512 mm. A 16th strand results inan elongation value of 11.8. What are thevalues of the sample mean and sample standarddeviation for all 16 elongation observations?

Answered: Image /qna-images/answer/689fd2de-36bd-4da1-a279-c8b3755f0763.jpg

76. Let X, and s denote the sample mean and variance for the sample xị, ... , X, and let xp+1 and s1 denote these quantities when an additional obser- vation x,41 is added to the sample. a. Show how xp+1 can be computed from x, and Xn+1• b. Show that n 151 = (n – 1)8, + - - (xn+1 – Xn)² n+1 so that s+1 can be computed from x,+1, Xp, and s. c. Suppose that a sample of 15 strands of drapery yarn has resulted in a sample mean thread elongation of 12.58 mm and a sample standard deviation of .512 mm. A 16th strand results in an elongation value of 11.8. What are the values of the sample mean and sample standard deviation for all 16 elongation observations?

76. Let X, and s denote the sample mean and variance for the sample xị, ... , X, and let xp+1 and s1 denote these quantities when an additional obser- vation x,41 is added to the sample. a. Show how xp+1 can be computed from x, and Xn+1• b. Show that n 151 = (n – 1)8, + - - (xn+1 – Xn)² n+1 so that s+1 can be computed from x,+1, Xp, and s. c. Suppose that a sample of 15 strands of drapery yarn has resulted in a sample mean thread elongation of 12.58 mm and a sample standard deviation of .512 mm. A 16th strand results in an elongation value of 11.8. What are the values of the sample mean and sample standard deviation for all 16 elongation observations?

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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Estimation

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76. Let ī, and s denote the sample mean and variance
for the sample x1, ... , X, and let īp+1 and s
denote these quantities when an additional obser-
vation x41 is added to the sample.
a. Show how xp+1 can be computed from x, and
'n+1
Xn+1.
b. Show that
ns
= (n – 1)s, +-
- (xn+1 – Xn)²
n+1
so that s can be computed from x,„41, Xn,
and s?.
'n+1
c. Suppose that a sample of 15 strands of drapery
yarn has resulted in a sample mean thread
elongation of 12.58 mm and a sample standard
deviation of .512 mm. A 16th strand results in
an elongation value of 11.8. What are the
values of the sample mean and sample standard
deviation for all 16 elongation observations?

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