(a) Generate 100 realisations of the sample variance of 10 independent N(0,1) random variables and store them in s2. (b) Plot the histogram of (10-1)*s2 and overlay it with the density function of the x distribution (use dchisq). (c) Repeat (a) and (b) with n = 60 independent N(0, 1) random variables. Over- lay the histogram with both the density curve of x2-1 and the density curve of N(n − 1, 2(n − 1)) (in two different colours). Comment on the fit. - (d) For n = 60, compute P((n − 1) · S² > 68) using both the exact distribution (x2-1) and the normal approximation. Compare the results.
(a) Generate 100 realisations of the sample variance of 10 independent N(0,1) random variables and store them in s2. (b) Plot the histogram of (10-1)*s2 and overlay it with the density function of the x distribution (use dchisq). (c) Repeat (a) and (b) with n = 60 independent N(0, 1) random variables. Over- lay the histogram with both the density curve of x2-1 and the density curve of N(n − 1, 2(n − 1)) (in two different colours). Comment on the fit. - (d) For n = 60, compute P((n − 1) · S² > 68) using both the exact distribution (x2-1) and the normal approximation. Compare the results.
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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Transcribed Image Text:(a) Generate 100 realisations of the sample variance of 10 independent N(0, 1)
random variables and store them in s2.
(b) Plot the histogram of (10-1)*s2 and overlay it with the density function of
the x distribution (use dchisq).
(c) Repeat (a) and (b) with n = 60 independent N(0, 1) random variables. Over-
lay the histogram with both the density curve of x2-1 and the density curve
of N(n − 1, 2(n − 1)) (in two different colours). Comment on the fit.
(d) For n = 60, compute P((n − 1) · S² > 68) using both the exact distribution
(x2-1) and the normal approximation. Compare the results.
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VIEWStep 3: Plot histogram of (10-1)*s2 and overlay it with the density function of chi square distribution.
VIEWStep 4: Repeat (a) and (b) with n = 60 independent N(0, 1) random variables.
VIEWStep 5: Simulate 100 realisations of the sample variance of 60 independent N(0, 1) random variables.
VIEWStep 6: Determine P((n − 1) · S² > 68) using both exact distribution and the normal approximation.
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