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0

From your conclusion, 1. is correct. But more specifically, it characterizes the nature of an underlying data generating statistic. A table of results of dice throws is likely iid, but more significantly it is because the dice roll itself is iid. Not really for 2. since you would be simply calculating for $P(A)P(B) = P(A,B)$ and $P(A) = P(B), \forall A, B$ ...

2

The point is even you know the distribution, sometimes you can't prove that the sampled data is i.i.d. or not! (more details in https://stats.stackexchange.com/q/130381/144441). Hence, without knowing the distribution, you have less information, and of course, you can't prove any identically distributedness property of the sampled data. Note that i.i.d. is ...

2

In general term yes. Because what the ML algorithms do in general is to learn the hidden probability density function of the target examples (cats, dogs..). And that is done by learning the conditional probability function between inputs, $X$, and target outputs, $y$, for discriminative models or by learning the joint probability function for generative ...

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