geometric distribution

• Expected Value of a Geometric Distribution by First-Step Analysis
  Use first-step analysis to derive the mean of a geometric waiting time, then see how the answer changes when you count failures instead of trials.
• 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.
• How to Prove the Variance of a Geometric Distribution
  Derive the geometric distribution’s variance, q/p², using its probability-generating function, and compare the trials and failures counting conventions.
• How to Prove the Variance of a Geometric Distribution
  Derive Var(X) = (1-p)/p² for a geometric random variable using its probability-generating function, and see how the 0-based convention differs.
• Expected Value of 1/(1 + X) for a Geometric Random Variable
  For a geometric random variable X, E[1/(1+X)] is -p ln(p)/(1-p) on support starting at zero; starting at one gives a different formula.