Question

if a coin is tossed twice the following outcomes are expected:
A={(H,H), (H,T), (T,H), (H,H)}
what will be domain & range in the context of this example?

Answer 1

Domain = { H,H,T,H}
Range ={ H,T,H,H}

Answer 2

For how and why, read a little bit about domain and range of functions.

Answer 3

I'll chime in here with the note that the domain can be written as \(\{H, T\}\) and the same with the range since sets don't contain repeating elements.

Answer 4

In probability terms I don't think it makes sense to talk about domain and range in the usual sense.
I think the domain is as written in the question
{(H,H), (H,T), (T,H), (H,H)} because that is the the list of possible outcomes.

Answer 5

thanks @estudier

Answer 6

shouldn't that then be the range if it's possible outcomes?

Answer 7

It seems to me as if
Domain = {H, T}
Range = {(H,H), (H,T), (T,H), (H,H)}
would be more correct then.

Answer 8

That is why I said I don't think it makes sense to use these terms as if it were a function (each element of the domain mapped to precisely one in the range)
I believe it is customary in probability to refer to the list of outcomes as the domain.

Answer 9

We COULD give the experiment a probability distribution, that would then be a function in the usual sense.

Answer 10

Yes, I think you're right.

Answer 11

@estudier when you refer to the list of outcomes as the domain. then do you mean all outcomes or just the set of desired events?

Answer 12

I mean the set of all possible outcomes (I think it is also referred to as the sample space)