# How can I calculate the total probability distribution function over many trials?

Say I have an experiment to determine the value of a certain parameter, $k$. I run the experiment once and I recover a probability distribution function for $k$. If I run is 20 times I get 20 distributions. How can I calculate the total probability distribution over all 20? Simply multiplying the pdf's together won't work, since even if the integral over a given pdf = 1, the integral over the product of all the pdf's need not be 1.

To clarify: assume, for example, that I have 20 different masses and one spring. For each mass, I hang the mass from the spring and determine a pdf for the spring constant (this is a contrived example, I know). Is there a way for me to then get the pdf of the spring that combined the data from all 20 experiments / masses?

• Why wouldn't you just combine the data and fit one distribution. Commented Aug 18, 2017 at 23:49
• If you run it once, 20, ... infinite times doesn't it coincide to be the Expected value of your distribution? According to the Law of Large Numbers Commented Aug 19, 2017 at 0:06
• Edited the original post to clarify my situation! Commented Aug 19, 2017 at 7:53