while the score is a function of formula_2, it also depends on the observations formula_8 at which the likelihood function is evaluated, and in view of the random character of sampling one may take its expected value over the sample space. under certain regularity conditions on the density functions of the random variables, the expected value of the score, evaluated at the true parameter value formula_2, is zero. to see this rewrite the likelihood function formula_10 as a probability density function formula_11, and denote the sample space formula_12. then: