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Is mean equal to expected value?

  1. Is mean equal to expected value?
  2. Why is mean called expected value?
  3. Is expectation always mean?

Is mean equal to expected value?

There's no difference. They are two names for the same thing. They tend to be used in different contexts, though. You talk about the expected value of a random variable and the mean of a sample, population or probability distribution.

Why is mean called expected value?

Essentially, the EV is the long-term average value of the variable. Because of the law of large numbers, the average value of the variable converges to the EV as the number of repetitions approaches infinity. The EV is also known as expectation, the mean or the first moment.

Is expectation always mean?

The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable takes on where the weighting is according to the relative frequency of occurrence of those individual values.

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