Question

What is difference between w mean and expected value?

Answer 1

Sometimes, they mean the same thing. For instance, if XX is a random variable then we can usually define the expected value EXEX of XX to be either the sum or the integral over the support of XX of xpX(x)xpX(x), where pXpX is the probability density or probability mass function. This is frequently called the mean of XX and in this context the terms may be used interchangeably. However, if you have a list of NN numbers a1,a2,…,aNa1,a2,…,aN, then the mean of that list of numbers is 1N(a1+a2+⋯+aN)1N(a1+a2+⋯+aN). This definition has nothing inherently to do with probability, and we wouldn't call this the "expected value" of the list. They are closely related however: if you have a list of numbers drawn from some probability distribution, then taking the mean of that list is usually a very good way to estimate the expected value of the probability distribution.