How is the probability density function of a continuous random variable computed? For example, how is the Gaussian pdf for a continuos random variable computed? If you were the first one to come up with Gaussian pdf, how might you have done it? Could you briefly explain it using an example?
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This might be a better fit for https://stats.stackexchange.com/ – Paul T. Aug 13 '21 at 14:11
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Good start would be the wikipedia pages which present the equations relating RVs, distribution functions, generating functions, etc. – Carl Witthoft Aug 13 '21 at 14:51
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First you must decide what continuous probability distribution best fits your problem: normal, exponential, lognormal,... Then you estimate the parameters of that particular distribution by taking samples from the population. The uncertainty in the estimated parameters can also be estimated. A good book on probability and statistics provides the details and examples; for example Dougherty's textbook Probability and Statistics for the Engineering, Computing, and Physical Sciences (Prentice-Hall).
John Darby
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