I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution probability for the possible values of the observable, which is better than only expectation values. So why do we claim that 'all we can get is expectation values'? Also, why cannot we model these uncertainties in the a priori knowledge of a measurement using random variables and probability language? Is it really necessary to go trough this whole formalism?

I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution probability for the possible values of the observable, which is better than only expectation values. So why do we claim that 'all we can get is expectation values'? Also, why cannot we model these uncertainties in the a priori knowledge of a measurement using random variables and probability language? Is it really necessary to go through this whole formalism?

I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory..but performing the same experiment many times would generate a distribution probability for the possible values of the observable which is better than only expectation values..so why we claim that 'all we can get is expectation values'? Also, why cannot model these uncertainties in the a priori knowledge of a measurement using random variables and probability language? is it really necessary to go trough this whole formalisms?

I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution probability for the possible values of the observable, which is better than only expectation values. So why do we claim that 'all we can get is expectation values'? Also, why cannot we model these uncertainties in the a priori knowledge of a measurement using random variables and probability language? Is it really necessary to go trough this whole formalism?

I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory..but performing the same experiment many times would generate a distribution probability for the possible values of the observable which is better than only expectation values..so why we claim that 'all we can get is expectation values' ?? Also, why cannot model these uncertainties in the a priori knowledge of a measurement using random variables and probability langage ? is it really necessary to go trough this whole formalisms  ? thanks in advance for your help.

I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory..but performing the same experiment many times would generate a distribution probability for the possible values of the observable which is better than only expectation values..so why we claim that 'all we can get is expectation values'? Also, why cannot model these uncertainties in the a priori knowledge of a measurement using random variables and probability language? is it really necessary to go trough this whole formalisms?