Can someone check my code, I am unsure if it is correct.

I'm getting a parabola for the normal distribution and no plot for the derivative.

Assignment

Download this file which computes the normal distribution:

norm_dist.mDownload norm_dist.m (it is this code) --->

function y = norm_dist(x)

y = exp(-x.^2/2)/sqrt(2*pi);

end

The code on top of this is the norm_dist mfile

The code under this is the assignment

% Start a script .m file with this line:

clear all; close all; clc; format compact

% Define this vector

x = -3: 0.1 : 3;

% Compute y:

y = norm_dist(x);

%% Open a figure and plot y as a function of x:

% Turn on the grid:

%% Use gradient() to compute the derivative

%% Then plot the gradient result on the same figure;

% If computed correctly:

% the derivative will be > 0 for x < 0

% the derivative will be = 0 for x = 0

% the derivative will be < 0 for x > 0

% Use the legend function to identify the 2 curves:

legend('Normal Distribution', 'derivative')

% Add this title:

title('Normal Distribution and its derivative')

My code

First Script

clear all; close all; clc; format compact

x = -3: 0.1 : 3;

y = norm_dist(x);
%% Open a figure and plot y as a function of x:
figure;
plot(x,y)
% Turn on the grid:
grid on

%% Use gradient() to compute the derivative
der_x = gradient(x)

der_x = 1×61

0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000

der_y = norm_dist(der_x)

der_y = 1×61

0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970 0.3970

%% Then plot the gradient result on the same figure;
hold on;
plot(der_x,der_y)

% If computed correctly: 
% the derivative will be > 0 for x < 0
% the derivative will be = 0 for x = 0
% the derivative will be < 0 for x > 0
% Use the legend function to identify the 2 curves:
legend('Normal Distribution', 'derivative')
% Add this title:
title('Normal Distribution and its derivative')

Second Script

function y = norm_dist(x)
y = exp(-x.^2/2)/sqrt(2*pi);
end

Answer 1

[Walter Roberson]

Your x is uniform increase. Its gradient is constant -- every entry is a fixed value greater than the one before.

You are plotting using that gradient as the x coordinate. But that means you are plotting using constant independent variable. If anything manages to get drawn, it would be entirely confined to that single constant value 0.1 as the coordinate of the independent variable.

You are asking for the normal distribution of the gradient of the x values. But the gradient is constant, so all of the normal distribution entries are the same. So your dependent variable der_y are all the same. So you end up plotting only a single point.

I think it likely you should not be taking the gradient of x, that you should be taking the gradient of y, and plotting the gradient of y with respect to x.

[Eduardo Gallegos]

You were absolutely correct, thank you.