# Binomial and poisson distribution questions and answers pdf

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- Probability Distributions
- Poisson Distribution — Intuition, Examples, and Derivation
- Exam Questions – Poisson distribution
- The Poisson and Binomial Distributions

## Probability Distributions

Sign in. Why did Poisson have to invent the Poisson Distribution? When should Poisson be used for modeling? To predict the of events occurring in the future! More formally, to predict the probability of a given number of events occurring in a fixed interval of time. It can be how many visitors you get on your website a day, how many clicks your ads get for the next month, how many phone calls you get during your shift, or even how many people will die from a fatal disease next year, etc. One way to solve this would be to start with the number of reads.

## Poisson Distribution — Intuition, Examples, and Derivation

The probability of a success during a small time interval is proportional to the entire length of the time interval. Apart from disjoint time intervals, the Poisson random variable also applies to disjoint regions of space. We use upper case variables like X and Z to denote random variables , and lower-case letters like x and z to denote specific values of those variables. The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:. Use Poisson's law to calculate the probability that in a given week he will sell.

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Normal distribution describes continuous data which have a symmetric distribution, with a characteristic 'bell' shape. Binomial distribution describes the distribution of binary data from a finite sample. Thus it gives the probability of getting r events out of n trials. Poisson distribution describes the distribution of binary data from an infinite sample. Thus it gives the probability of getting r events in a population. One such example is the histogram of the birth weight in kilograms of the 3, new born babies shown in Figure 1.

(b) Use the normal approximation to binomial distribution to answer question (a). (c) Repeat question (b) but for a survey of people, where 55% prefer A. 3. A.

## Exam Questions – Poisson distribution

In probability theory, the normal distribution or Gaussian distribution is a very common continuous probability distribution. The normal distribution is sometimes informally called the bell curve. Probability density function or p.

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The Poisson Distribution is a discrete distribution. It is named after Simeon-Denis Poisson , a French mathematician, who published its essentials in a paper in The Poisson distribution and the binomial distribution have some similarities, but also several differences. The binomial distribution describes a distribution of two possible outcomes designated as successes and failures from a given number of trials. The Poisson distribution focuses only on the number of discrete occurrences over some interval.

### The Poisson and Binomial Distributions

Basic Concepts. Definition 1 : The Poisson distribution has a probability distribution function pdf given by. Figure 1 — Poisson Distribution. Observation : Some key statistical properties of the Poisson distribution are:. Excel Function : Excel provides the following function for the Poisson distribution:.

Assume that a large Fortune company has set up a hotline as part of a policy to eliminate sexual harassment among their employees and to protect themselves from future suits. This hotline receives an average of 3 calls per day that deal with sexual harassment. Obviously some days have more calls, and some have fewer.

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The random variable X is said to have a binomial distribution with parameters n and p; abbreviated. X ∼ Bin(n, p) The Binomial Distribution: Example Check your answers using the standard results E[Y ] = np and Var [Y ] = np(1p).