Definition

In a series of Bernoulli trials, random variable XX that equals the number of trials needed to have the first success (that the xx-th trial is the first success) is a geometric random variable with parameter 0<p<10 < p <1, where probability mass function is given by

P(X=x)=(1−p)x−1pP(X=x) = (1-p)^{x-1}p

for x=1,2,...x = 1,2,...

See also

References

  1. https://gauss.vaniercollege.qc.ca/~maks/H22_HTH/Notes/L15_HTH_Mak.pdf
  2. https://en.wikipedia.org/wiki/Geometric_distribution
  3. https://mathworld.wolfram.com/GeometricDistribution.html