how to calculate the exponential distribution in matlab

To generate random numbers following an exponential distribution in MATLAB, you can use the exprnd function from the Statistics and Machine Learning Toolbox. The syntax for exprnd is:

main.m
X = exprnd(mu, m, n)
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where mu is the mean of the distribution, and m and n specify the size of the output array. X will be an array of size m-by-n containing random numbers generated from an exponential distribution with mean mu.

For example, to generate 1000 random numbers from an exponential distribution with mean 2, you can use the following code:

main.m
mu = 2;
X = exprnd(mu, 1, 1000);
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You can also plot the probability density function (pdf) and cumulative distribution function (cdf) of the exponential distribution using the exppdf and expcdf functions, respectively:

main.m
x = linspace(0, 10, 100);
pdf = exppdf(x, mu);
cdf = expcdf(x, mu);

subplot(1, 2, 1);
plot(x, pdf);
title('Exponential PDF');
xlabel('x');
ylabel('f(x)');

subplot(1, 2, 2);
plot(x, cdf);
title('Exponential CDF');
xlabel('x');
ylabel('F(x)');
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This will generate a plot with the pdf and cdf of the exponential distribution with mean 2, ranging from 0 to 10.