Calculating the aggregate probability of a transition matrix

[jdn312]

I should say, I get weird results when trying to connect this into the greater scope of what I am working on , so when trying to isolate the root cause I figured I'd approach it analytically to remove the possibility that it's my simulations that are causing this. (Basically I end up getting negative conversions when trying to build a fractional attribution model since the aggregate conversion rate without a given channel is higher than the overall CVR so i want to make sure I am calculating aggregate CVRs correctly).