Why we find expectation value?

[rida]

why we find expectation value?

why do we take expectation value of sime entity? and how come we know that our expected value is correct

 

[kith]

If you have a random process which generates experimental outcomes, you cannot predict the individual outcome. If you know the probability distribution, you can however calculate what you will get on average. This is the expectation value.

If you average the outcomes of many repetitions of the experiment, you get the mean value. This mean value converges to the expectation value if you increase the number of repetitions.