I have a model of total reaction time T, which is a composite of a selection time S and a discrimination time D. So a person first finds something, this takes the tS. Then he discriminates and reports an attribute of this thing, this takes the time D. We only measure the total time T, though. So, my model for T is:
T = S + D
In considering, I try to think about how these random variables behave in simplified settings; and these are my questions:
1.) If I would define S and D to be independent, could I infer that S and T, or D and T are independent? If not, could I infer that D and T are conditionally independent, given S?
2.) Defining S and D to be independent and normally distributed, I know I can infer that T is normally distributed. But what if I define T and D as normally distributed, can I infer that S is normally distributed? I think this boils down to the question 1.) whether I can say that T and D are independent.