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:

    “In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
    —Michel de Montaigne (1533–1592)

    “There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
    —Bernard Mandeville (1670–1733)

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