Is there a closed form CDF for the sum of two triangularly distributed random variables? To calculate the PDF of the sum of two triangularly distributed random variables all I did was add them together and divided by two:
$\dfrac{f(x, a1, b1, c1) + f(x, a2, b2, c2)}{2}$

And implementing it in Python gets me the following PDF:

My issue was with the CDF. Addition doesn't work, but I don't know how to mathematically derive a closed form for it:


If you have the probability density function $$\dfrac{f(x, a1, b1, c1) + f(x, a2, b2, c2)}{2}$$ then the cumulative distribution function will be $$\dfrac{F(x, a1, b1, c1) + F(x, a2, b2, c2)}{2}$$
We can't see how you generated the CDF in your image and it seems like a computation error.

Sidenote: You added the two pdf functions together. That is what you do with a mixture of variables. This is not what you do to compute a sum of two random variables, for a sum of random variables you use convolution.
