# How Do You Update the Probability Density Function Given That the?

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## Easy-to-use PDF software     ## How do you update the probability density function given that the value is greater than a constant?

You want to know the probability that the difference between the random variables is negative. To get PDF of the sum of the two variables, you simply take the convolution of their PDFs. So to get the PDF of their difference, convolve the PDF of one with the PDF of the negation of the other. If you have PDFs f(x) and g(x), the PDF for the difference between the variables is f(x)*g(-x). Just integrate this convolution from 0 to \infty to find the probability that the variable drawn from the distribution represented by f is larger. Example. let f(x) = 2x and g(x) = 1 be two PDFs valid for x between 0 and 1, and 0 elsewhere. For x between 0 and 1, the convolution is (f(x)*g(-x))(t) = (t)=1-t^2. Above 1, itâs 0. Integrating this for all positive values, we get 2/3.

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