Likelihood

• What Is the Fisher Information for an Exponential Distribution?
  For an exponential distribution, Fisher information is 1 over the squared rate per observation, or n over the squared rate for n iid observations.
• What Is the Fisher Information of a Geometric Distribution?
  For a geometric random variable with success probability p, the Fisher information is 1/[p²(1−p)] per observation and n times that for n observations.
• What Is the Fisher Information of a Binomial Distribution?
  For X ~ Binomial(n,p), Fisher information about p is n/[p(1-p)]. Derive it, compare parameterizations, and see a worked example.
• What Is the Fisher Information of a Normal Distribution?
  For n independent normal observations, the Fisher information is diagonal: n/σ² for the mean and n/(2σ⁴) for the variance.
• What Is the Fisher Information of the Rayleigh Distribution?
  For the standard Rayleigh scale parameter, one observation has Fisher information 4 divided by sigma squared; n independent observations have 4n divided by sigma squared.