I'm trying to make a set of Gaussians, then I want to plot each gaussian seperately and compare them to how they look combined. I currently have it where I only look at the combined case:
G[x_] := Sum[a[i] Exp[ -(x - b[i])^2/(2 c[i]^2)], {i, 10}]; Do[Print[{a[i] = RandomInteger [{1, 10}], b[i] = RandomInteger[{-10, 10}], c[i] = RandomInteger[{1, 10}]}], {i, 10}] Plot[{G[x]}, {x, -10, 10}, PlotRange -> All]
Basically I'm making a total function G[x] and I'm summing 10 randomly generated functions. My end goal is to enter my own values but for now this will work. Now I want to take these random functions and name them somethings like A1[x], A2[x] A3[x], or however the syntax will allow so I can easily tell function 1 is related to a[1],b[1],and c[1]. Then I want to plot all the Ai[x] functions along with the G[x] function so I can see each individual functions contributio. What kind of look do i need to make to generate this subset of functions that comprise G[x]?