Greetings, Friends.

I have a function f[t] which is a density function. It has a [0,2] interval and integrates to unity. I convolve f[t] with itself to get g[t]. It has a [0,4] interval and integrates to unity. All is well with that and I understand.

BUT, the boundary of g[t] shouild be on the interval [0,4/Sqrt[3]]. This is based upon both simulation and other analyses.

At present, the area of the g[t] function on the [4/Sqrt[3], 4] interval accounts for 1.4087% of the area under the curve. Not a "trivial" or "throwaway" amount.

Does anyone know of a way to "re-scale" or modify my convolved result g[t] so that all of the resultant area under the curve is on the [0,4/Sqrt[3]] interval?

My work is attached.