Still none the wiser [General Sta­tis­tics]

Hi Helmut,

thanks for trying. I have to admit, I am sorry but I am none the wiser.
Let us go over it again:
Let x be our sample.
Let f(x|other shit) be a function of x, given some other shit.
Let g(x|other shit) be another function of x, given the same other shit.

In general (and ideally layman's) terms, what properties of f and g would lead me to think f and g are independent.

I assume it is implied that we are talking about independence from each other, at least when we try and think of f and g as numerators and denominators of the quantity defining t above. When this is the wrong perception, kindly correct me, please.

Pass or fail!
ElMaestro