Probability-generating Function - Examples

Examples

  • The probability-generating function of a constant random variable, i.e. one with Pr(X = c) = 1, is
  • The probability-generating function of a binomial random variable, the number of successes in n trials, with probability p of success in each trial, is
Note that this is the n-fold product of the probability-generating function of a Bernoulli random variable with parameter p.
  • The probability-generating function of a negative binomial random variable, the number of trials until the rth success with probability of success in each trial p, is
(Convergence for ).
Note that this is the r-fold product of the probability generating function of a geometric random variable.
  • The probability-generating function of a Poisson random variable with rate parameter λ is


Read more about this topic:  Probability-generating Function

Famous quotes containing the word examples:

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)

    “It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
    —G.C. (Georg Christoph)

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)