I would do electronics, computer science & mathematical statistics, but then get some deep subject knowledge in a soft domain that really interests you (e.g. med, biochem, genetics, pharmacology, neuroscience etc).
There are soooo many problems out there just waiting to be solved by skilled engineers/mathematicians/statisticians, but the sad thing is that most of these people have no subject matter knowledge, and therefore are ignorant of the opportunities. Likewise the subject matter experts without the statistical/engineering background are unable to grasp what could be done, so never even contemplate the questions. Even "top" researchers in some of my fields are completely unaware of the possibilities. They are ignorant and unaware of it, and sadly even collaborations do not seem to help.
There's gold in the intersections of disciplines.
Edit: But, this is only one approach, and assumes that you want to break new scientific ground as well as make money.
I totally agree with your statement that "There's gold in the intersections of disciplines.", and I've put it down on my list of things to become (a polymath).
I've quite seriously looked at the medical sector as one that lacks technological innovation, and both this answer, in addition to makerman's answer seem to validate that opinion.
Look where things lack innovation seems to be the best way to go.
There are soooo many problems out there just waiting to be solved by skilled engineers/mathematicians/statisticians, but the sad thing is that most of these people have no subject matter knowledge, and therefore are ignorant of the opportunities. Likewise the subject matter experts without the statistical/engineering background are unable to grasp what could be done, so never even contemplate the questions. Even "top" researchers in some of my fields are completely unaware of the possibilities. They are ignorant and unaware of it, and sadly even collaborations do not seem to help.
There's gold in the intersections of disciplines.
Edit: But, this is only one approach, and assumes that you want to break new scientific ground as well as make money.