The Poisson probability distribution, named after the French mathematician SiméonDenis. Poisson is another important probability distribution of a discrete random variable that has a large number of applications. Suppose a washing machine in a Laundromat breaks down an average of three times a month. We may want to find the probability of exactly two breakdowns during the next month. This is an example of a Poisson probability distribution problem. Each breakdown is called an occurrence in Poisson probability distribution terminology. The Poisson probability distribution is applied to experiments with random and independent occurrences. The occurrences are random in the sense that they do not follow any pattern, and, hence, they are unpredictable. Independence of occurrences means that one occurrence (or nonoccurrence) of an event does not influence the successive occurrences or nonoccurrences of that event. The occurrences are always considered with respect to an interval. In the example of the washing machine, the interval is one month. The interval may be a time interval, a space interval, or a volume interval. The actual number of occurrences within an interval is random and independent. If the average number of occurrences for a given interval is known, then by using the Poisson probability distribution, we can compute the probability of a certain number of occurrences, x, in that interval. Note that the number of actual occurrences in an interval is denoted by x.
The following three conditions must be satisfied to apply the Poisson probability distribution. 1. x is a discrete random variable.
2. The occurrences are random.
3. The occurrences are independent.
The following are three examples of discrete random variables for which the occurrences are random and independent. Hence, these are examples to which the Poisson probability distribution can be applied. 1. Consider the number of telemarketing phone calls received by a household during a given...
...The Poissondistribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business, number of customers in waiting lines, number of defects in a given surface area, airplane arrivals, or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies, e.g., to model the number of prairie dogs found in a square mile of prairie. The...
...Probabilitydistribution
Definition with example:
The total set of all the probabilities of a random variable to attain all the possible values. Let me give an example. We toss a coin 3 times and try to find what the probability of obtaining head is? Here the event of getting head is known as the random variable. Now what are the possible values of the random variable, i.e. what is the possible number of times that head might occur?...
...Binomial, Bernoulli and PoissonDistributions
The Binomial, Bernoulli and Poissondistributions are discrete probabilitydistributions in which the values that might be observed are restricted to being within a predefined list of possible values. This list has either a finite number of members, or at most is countable.
* Binomial distribution
In many cases, it is appropriate to...
...Statistics
Chapter 5
Some Important Discrete
ProbabilityDistributions
51
Chapter Goals
After completing this chapter, you should be able
to:
Interpret the mean and standard deviation for a
discrete probabilitydistribution
Explain covariance and its application in finance
Use the binomial probabilitydistribution to find
probabilities
Describe when to apply the binomial...
...Tutorial on Discrete ProbabilityDistributions
Tutorial on discrete probabilitydistributions with examples and detailed solutions.

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 Let X be a random variable that takes the numerical values X1, X2, ..., Xn with probablities p(X1), p(X2), ..., p(Xn) respectively. A discrete probability...
...POISSONDISTRIBUTION
Many studies are based on counts of the times a particular event occurs in a given area of opportunity. An area of opportunity is a continuous unit or interval of time, volume, or any physical area in which there can be more than one occurrence of an event. Examples of variables that follow the Poissondistribution are the surface defects on a new refrigerator, the number of network failures in a day, the number...
...Discrete and Continuous Probability
All probabilitydistributions can be categorized as discrete probabilitydistributions or as continuous probabilitydistributions (stattrek.com). A random variable is represented by “x” and it is the result of the discrete or continuous probability. A discrete probability is a random variable that can either be a finite or...
...ProbabilityDistribution Essay
Example Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH, HT, TH, and TT. Now, let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0, 1, or 2, so it is a discrete random variable
Binomial Probability Function: it is a discrete distribution. The...