For the continuous distributions, does it make sense to ask the probability at a certain point say Pr(X = a) or is it usually more in the form of Pr(a <= X <= b)? How would we deal with this Pr(X = a) case would we just integrate from a - epsilon to a + epsilon?
pw123
@oadrian96 I think Pr(X = a) = 0 for a continuous distribution because the area under that point is 0. I would double check this though.
barath
For X = a, a single random point, the area under the curve will be similar to 'area of a line' which is essentially 0. If my intuition is wrong, please correct me. Thanks
Osoii
This reminds me of a saying that an event is still probable to happen, even its probability is 0.
jacheng
@barath yeah that makes sense, because it's a continuous function, you have to integrate under the curve for a range to get a probability, otherwise the probability of each event is 0 since there are infinitely many possible events
For the continuous distributions, does it make sense to ask the probability at a certain point say Pr(X = a) or is it usually more in the form of Pr(a <= X <= b)? How would we deal with this Pr(X = a) case would we just integrate from a - epsilon to a + epsilon?
@oadrian96 I think Pr(X = a) = 0 for a continuous distribution because the area under that point is 0. I would double check this though.
For X = a, a single random point, the area under the curve will be similar to 'area of a line' which is essentially 0. If my intuition is wrong, please correct me. Thanks
This reminds me of a saying that an event is still probable to happen, even its probability is 0.
@barath yeah that makes sense, because it's a continuous function, you have to integrate under the curve for a range to get a probability, otherwise the probability of each event is 0 since there are infinitely many possible events