The symmetry or skewness (lack of symmetry) of adistribution is often measured by means of the quantity α3 = μ3σ3 Use the formula for μ3 obtained in Exercise 25 to deter-mine α3 for each of the following distributions (which have equal means and standard deviations):(a) f(1) = 0.05, f(2) = 0.15, f(3) = 0.30, f(4) = 0.30,f(5) = 0.15, and f(6) = 0.05;(b) f(1) = 0.05, f(2) = 0.20, f(3) = 0.15, f(4) = 0.45,f(5) = 0.10, and f(6) = 0.05.Also draw histograms of the two distributions and notethat whereas the first is symmetrical, the second has a“tail” on the left-hand side and is said to be negativelyskewed.
The symmetry or skewness (lack of symmetry) of adistribution is often measured by means of the quantity α3 = μ3σ3 Use the formula for μ3 obtained in Exercise 25 to deter-mine α3 for each of the following distributions (which have equal means and standard deviations):(a) f(1) = 0.05, f(2) = 0.15, f(3) = 0.30, f(4) = 0.30,f(5) = 0.15, and f(6) = 0.05;(b) f(1) = 0.05, f(2) = 0.20, f(3) = 0.15, f(4) = 0.45,f(5) = 0.10, and f(6) = 0.05.Also draw histograms of the two distributions and notethat whereas the first is symmetrical, the second has a“tail” on the left-hand side and is said to be negativelyskewed.
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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Question
The symmetry or skewness (lack of symmetry) of a
distribution is often measured by means of the quantity
distribution is often measured by means of the quantity
α3 = μ3
σ3
σ3
Use the formula for μ3 obtained in Exercise 25 to deter-
mine α3 for each of the following distributions (which
mine α3 for each of the following distributions (which
have equal means and standard deviations):
(a) f(1) = 0.05, f(2) = 0.15, f(3) = 0.30, f(4) = 0.30,
f(5) = 0.15, and f(6) = 0.05;
(b) f(1) = 0.05, f(2) = 0.20, f(3) = 0.15, f(4) = 0.45,
f(5) = 0.10, and f(6) = 0.05.
Also draw histograms of the two distributions and note
that whereas the first is symmetrical, the second has a
“tail” on the left-hand side and is said to be negatively
skewed.
(a) f(1) = 0.05, f(2) = 0.15, f(3) = 0.30, f(4) = 0.30,
f(5) = 0.15, and f(6) = 0.05;
(b) f(1) = 0.05, f(2) = 0.20, f(3) = 0.15, f(4) = 0.45,
f(5) = 0.10, and f(6) = 0.05.
Also draw histograms of the two distributions and note
that whereas the first is symmetrical, the second has a
“tail” on the left-hand side and is said to be negatively
skewed.
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