Homework Help is Here – Start Your Trial Now!
Math
Statistics
Are the distributions the same?

Are the distributions the same?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
100%

This is a Statistics problem.

Are the distributions the same?

 

Compare the pdf of 22, where Z - Norm(0, 1) to the pdf of a normal random variable with mean 0 and standard deviation 2. We already saw how to estimate the pdf of 2Z, we just need to plot the pdf of Norm(0, 2) on the same graph. We show how to do this using both the histogram and the density plot approach. The pdf f(x) of Norm(0, 2) is given in R by the function f(x) = dnorm(r, 0, 2). hist(twoz, probability = TRUE, main = "Density and histogram of 22", xlab = "22" curve(dnorm(x, 0, 2), add = TRUE, col = "red") Density and histogram of 2Z Since the area of each rectangle in the histogram is approximately the same as the area under the curve over the same interval, this is evidence that 2Z is normal with mean 0 and standard deviation 2. Next, let's look at the density estimation together with the true pdf of a normal rv with mean 0 and o = 2. plot(density(twoZ), xlab = "2Z", main = "Density 2z and No rm (0, 2)" curve(dnorm (x, 0, 2), add = TRUE, col = "red") Density 2Z and Norm(0, 2) -5 Wow! Those look really close to the same thing! This is again evidence that 2Z - Norm(0, 2). Density 0.10 0.20 0.20 00'0 00'0
Transcribed Image Text:Compare the pdf of 22, where Z - Norm(0, 1) to the pdf of a normal random variable with mean 0 and standard deviation 2. We already saw how to estimate the pdf of 2Z, we just need to plot the pdf of Norm(0, 2) on the same graph. We show how to do this using both the histogram and the density plot approach. The pdf f(x) of Norm(0, 2) is given in R by the function f(x) = dnorm(r, 0, 2). hist(twoz, probability = TRUE, main = "Density and histogram of 22", xlab = "22" curve(dnorm(x, 0, 2), add = TRUE, col = "red") Density and histogram of 2Z Since the area of each rectangle in the histogram is approximately the same as the area under the curve over the same interval, this is evidence that 2Z is normal with mean 0 and standard deviation 2. Next, let's look at the density estimation together with the true pdf of a normal rv with mean 0 and o = 2. plot(density(twoZ), xlab = "2Z", main = "Density 2z and No rm (0, 2)" curve(dnorm (x, 0, 2), add = TRUE, col = "red") Density 2Z and Norm(0, 2) -5 Wow! Those look really close to the same thing! This is again evidence that 2Z - Norm(0, 2). Density 0.10 0.20 0.20 00'0 00'0
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS