The Binomial, Bernoulli and Poisson distributions are discrete probability distributions in which the values that might be observed are restricted to being within a pre-defined 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 summarize a group of independent observations by the number of observations in the group that represent one of two outcomes. For example, the proportion of individuals in a random sample who support one of two political candidates fits this description. In this case, the statistic is the count X of voters who support the candidate divided by the total number of individuals in the group n. This provides an estimate of the parameter p, the proportion of individuals who support the candidate in the entire population. The binomial distribution describes the behavior of a count variable X if the following conditions apply: the number of observations n is fixed, each observation is independent and represents one of two outcomes ("success" or "failure") and if the probability of "success" p is the same for each outcome. If these conditions are met, then X has a binomial distribution with parameters n and p, abbreviated B(n,p).

* Bernoulli distribution
In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli, is a discrete probability distribution The distribution of a discrete random variable taking two values, usually 0 and 1. An experiment or trial that has exactly two possible results, often classified as 'success' or 'failure', is called a Bernoulli trial. If the probability of a success is p and the number of successes in a single experiment is the random variable X, then X is a Bernoulli variable (also called a binary variable) and is said to have a Bernoulli distribution with parameter p. A binomial variable with...

...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...

...
A useful distribution for ﬁtting discrete data: revival
of the Conway–Maxwell–Poissondistribution
Galit Shmueli,
University of Maryland, College Park, USA
Thomas P. Minka and Joseph B. Kadane,
Carnegie Mellon University, Pittsburgh, USA
Sharad Borle
Rice University, Houston, USA
and Peter Boatwright
Carnegie Mellon University, Pittsburgh, USA
[Received June 2003. Revised December 2003]
Summary. A useful discrete...

...The BinomialDistribution
October 20, 2010
The BinomialDistributionBernoulli Trials
Deﬁnition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure.
1
Tossing a coin and considering heads as success and tails as failure.
The BinomialDistributionBernoulli Trials
Deﬁnition A...

...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...

...The Poisson probability distribution, named after the French mathematician Siméon-Denis. 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...

...#1 True or false: Even if the sample size is more than 1000, we cannot always use the normal approximation to binomial.
Solution:
If a sample is n>30, we can say that sample size is sufficiently large to assume normal approximation to binomial curve.
Hence the statement is false.
#2
A salesperson goes door-to-door in a residential area to demonstrate the use of a new Household appliance to potential customers. She has found from her years of...

...Probability distribution
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? It is 0 (head never occurs), 1 (head...

...standard deviation = square root of variance = sqrt(846) = 29.086 4. If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66 Draw a stem and leaf. Discuss the shape of the distribution. Solution: 2 3 4 5 6 | | | | | 219200 48714 0197 6
This distribution is right skewed (positively skewed) because the “tail” extends to the right. 5. What type of relationship is shown by this scatter plot?
45 40 35 30 25 20 15 10 5 0 0 5...

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