Discrete probability distributions random Poisson distribution

Since distributions describing a discrete random variable may be less familiar than those routinely used for describing a continuous random variable, a presentation of basic theory is warranted. Count data, expressed as the number of occurrences during a specified time interval, often can be characterized by a discrete probability distribution known as the Poisson distribution, named after Simeon-Denis Poisson who first published it in 1838. For a Poisson-distributed random variable, Y, with mean X, the probability of exactly y events, for y = 0,1, 2,..., is given by Eq. (27.1). Representative Poisson distributions are presented for A = 1, 3, and 9 in Figure 27.3. 

The Poisson distribution can be used to determine probabilities for discrete random variables where the random variable is the number of times that an event occurs in a single trial (unit of lime, space, etc.). The probability function for a Poisson random variable is... 

Probability mass function. A function which assigns a probability to values of a random variable. Used for discrete variables as opposed to probability density function, which is used for continuous ones. An example is given in the entry under Poisson distribution. 

Poisson distribution A probability distribution for a discrete random variable. It is defined, for a variable (r) that can take values in the range 0,1,2,. and has a mean value p, as... 

Poisson Distribution n A probability distribution of a discrete random variable, X, with non-negative integer values, X, that have a probability, P(x), of the form ... 

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