random variable with normal distribution

how can i find the first five moments of a random variable with pdf gaussisn distribution , and finding the characteristic function all in matlab?

Answer 1

[Image Analyst]

To get a bunch of random numbers drawn from a normal distribution, use randn().

r = randn(...........

If you want the nth moment just take the nth root of the sum of the values and divide by the number of samples minus 1.

If you want the central moments, then subtract the mean before raising to a power.

Sounds like homework (so I didn't give the actual MATLAB code, which is actually pretty simple - just a single line of code). Is it homework?

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[saif yahya]

yes it is a homework

[saif yahya]

the random variable x is defined by gaussian pdf has a support region x =[a,b], also with specific mean and standard deviation . how to use randn function to define this pdf, and how to find the moments (Mn)

[Image Analyst]

Didn't they go over the formula in class? Here is some code including the Wikipedia definition:

fprintf('Beginning to run %s.m ...\n', mfilename);

% https://en.wikipedia.org/wiki/Moment_(mathematics)#Sample_moments

mu = 50;
sigma = 10;
numSamples = 1000000;
r = mu + sigma * randn(1, numSamples);
meanr = mean(r)
sdr = std(r)
histogram(r);
grid on;
xlabel('r')
ylabel('Count');
caption = sprintf('Mu = %.2f, SD = %.2f', mu, sigma);
title(caption);

% Find second moment
n = 2
mom = sum(r.^n) / (numSamples-1)
% Find second central moment
momCentral = sum((r - meanr).^n) / (numSamples-1)

fprintf('Done running %s.m ...\n', mfilename);

You simply need to put into a for loop over n and index the two moments by the loop index. Just add 2 lines of code and take one away. Beware than many universities employ plagiarism detectors.

[saif yahya]

thank you very much.do you know how to find the characteristic function of this random variable ?

[Image Analyst]

Use histogram() with the 'pdf' option to describe it numerically. Analytically it's the Gaussian function.

[saif yahya]

if the above random variable r you defined by randn is truncated to have a region support r=[40,150] how to define the new pdf

[Image Analyst]

histogram() will give you the actual, empirical pdf. Not some theoretical analytical function. So the values don't matter. Support doesn't matter. You get what the PDF actually IS.