Solution Found!
Use a computer to plot the function xne?x and the Gaussian
Chapter , Problem 12P(choose chapter or problem)
Problem 12P
Use a computer to plot the function xne−x and the Gaussian approximation to this function, for n = 10, 20, and 50. Notice how the relative width of the peak (compared to n) decreases as n increases, and how the Gaussian approximation becomes more accurate as n increases. If your computer software permits it, try looking at even higher values of n.
Questions & Answers
QUESTION:
Problem 12P
Use a computer to plot the function xne−x and the Gaussian approximation to this function, for n = 10, 20, and 50. Notice how the relative width of the peak (compared to n) decreases as n increases, and how the Gaussian approximation becomes more accurate as n increases. If your computer software permits it, try looking at even higher values of n.
ANSWER:
Solution to 12P
Step 1
f(x)=xne-x is a gaussian approximation function which reaches maximum value when x=n. We are using Matlab to plot the function. For N=10,20 and 50. The relative width of the gaussian curve is decreased as n increased and the gaussian approximation becomes more accurate as n increases.
Matlab Code:
clear all
clf
clc
x = 0:.01:100;
plot(x,((x.^10).*exp(-x))/max((x.^10).*exp(-x)),'-g');hold on;
plot(x,((x.^20).*exp(-x))/max((x.^20).*exp(-x)),'-r');hold on;
plot(x,((x.^50).*exp(-x))/max((x.^50).*exp(-x)),'-k');hold on;
xlabel('n')
ylabel('x.^n.*exp(-x)')
title('plot of gaussian approximation for N=10,20 and 50')
legend('N=10','N=20','N=50')
grid on;