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Why are there two ways to write PDF and CDF functions?
To summarize the answers so far in brief. If you have the equation of the cumulative density function (cdf), try to use calculus to derive the analytical form of its first derivative. That produces the equation for the probability density function (pdf). If not, you can use subtraction (‘finite differences’?) to get from the cdf the value of the pdf at each value of x. For example, in an Excel spreadsheet. put the original values of x in Column A and the corresponding values of cdf(x) in Column B; then in Cell C2 place the formula =(B2-B1)/(A2-A1), then copy and paste the formula to the cells below C3.
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Now use the subtraction formula to get the value of the PDF. It's pretty similar in every cell that you use as input. As an example of how to find the PDF of the cumulative density function, write a short function in XLS format to do it (see Example in section of the main Spreadsheet Tutorial). If the CDF formula doesn't work, it's because the problem is not a simple derivative problem. For the CDF formula to work well in a problem like this, you also have to solve a more challenging problem with your knowledge of the differential equations for the continuous variables, where you also have to solve for the first derivative. Here are answers to those questions. When to use a PDF ? In almost any problem, you won't have the full solution. If you can get a partial or general solution of a problem such.