what does it mean to say data are drawn from a probability distribution P?
A random variable is something that takes different values where there is some randomness to the value it can take. A probability distribution assigns a probability to each possible outcome of that random variable. In your case, you are observing data that could've been different. In other words, if you took another sample with the same sample size you'd likely observe something different. Hence what you observe is considered random.
If your random variable is discrete, a probability distribution gives you a rule for the probability of each discrete value your random variable can take. If your random variable is continuous, it gives you a rule for the probability of any range of values your random variable can take.
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