I have seen that expected value of a discrete random variable is equal to the arithmetic mean of the distribution provided the values it takes. Is it true for all random variables irrespective of the distribution? Is there a case or example where expected value differs from the arithmetic mean?
Secondly I think it applies only for discrete random variables. I think for continuous random variables, the pdf is zero at particular points. So in that case can I say that expected value is not equal to the mean of random variable?