The Fisher information in an observation 
about a scalar parameter 
is the variance of the score function. If 
has probability
density function 
,
it is
![I(theta)=E_(theta)[(partial/(partialtheta)lnf(X;theta))^2].](/images/equations/FisherInformation/NumberedEquation1.svg) |
Under regularity conditions that permit differentiation under the integral sign, this can also be written as
![I(theta)=-E_(theta)[(partial^2)/(partialtheta^2)lnf(X;theta)].](/images/equations/FisherInformation/NumberedEquation2.svg) |
Fisher information is additive for independent observations. Thus, 
independent observations from the same distribution have information
.
The reciprocal of the information gives the Cramér-Rao
bound on the variance of an unbiased estimator
under corresponding regularity conditions.
