Question

Let X, Y, Z be independent jointly continuous random variables, and let g, h, r be some functions. For each one of the following formulas, state whether it is true for all choices of the functions g, h, and r, or false (i.e., not true for all choices of these functions). Do not attempt formal derivations; use an intuitive argument.

Answer 1

well, clearly I am to infer that it is false that they are all true.
Or not ...