[fabiom]

Interesting. But by the title I thought it was about an algebra (or algebraic structure) of random variables.

[wvlia5]

It presents how every F defined on random variables maps to a F' defined on the probability distribution of such random variables, an isomorphism.

[sasaf5]

I think parent was expecting to see things like operations between random variables and their typing system. I am trying to imagine how all of this could be derived from the isomorphism presented, but it's beyond my mathematical reach.