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Yes. And in any symmetric distribution, they will.
No.It is asymmetric.
yes it is
It can do. If you define a quarter of it as one part and the rest as another, the two WILL be different! But the distribution IS symmetric about its mean.
It is a probability distribution in which the probability of the random variable being in any interval on one side of the mean (expected value) is the same as for the equivalent interval on the other side of the mean.