what formula is this

[s.kishore1998]

In the attached image there is a formula. I remember the formula, but I can't remember what is that formula or what that formula gives.
I guess its something around mean but mean is just sum of probabilities/no of samples.
Thank you in advance for helping

 

[Cubist]

Your formula gives the expected value of x. It's more usually quoted without a denominator (because you'd normally consider all possible values for x and then the denominator will be 1).