Discreet Probability Distribution

Discreet probability distribution is that type of probability distribution that refers to the discreet type of random variables that deal with some different kinds of discreet probability distribution.

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A uniform distribution in discreet probability distribution mainly consists of the range that is basically from [1, n]. This discreet probability distribution has a probability mass function (pmf) which is given by the following:

P(X=x)=1/n, for x = 1 …. n. This type of discreet probability distribution has a parameter that is denoted by ‘n.’ This type of discreet probability distribution generally belongs to the set of all positive integers. This type of discreet probability distribution is basically applicable in cases where an experiment consisting of throwing dice or a deck of cards, etc. is involved. In this discreet probability distribution, X is the random variable.

A Bernoulli distribution is also a type of discreet probability distribution, and it consists of the parameter ‘p’ and has the probability mass function (pmf) of P(X=x)= px (1-p)1-x, for x = 0,1. In this discreet probability distribution, X is the random variable.

In this type of discreet probability distribution, the parameter ‘p’ mainly satisfies the two types of values, i.e. 0 and 1. This discreet probability distribution is applicable in cases where the outcomes are dichotomous in nature, i.e. either success or failure.

The discreet probability distribution, called binomial distribution, assumes the non negative values and its probability mass function (pmf) is given by the following:

P(X=x)=(ncx) pxqn-x, x = 0,1 …. n;q=1-p.

This discreet probability distribution mainly deals with cases like the tossing of a coin.
The discreet probability distribution, called Poisson distribution, has the probability mass function (pmf) that is as follows:

P(X=x)=e-α αx/x!, x=0,1,…… where X in the pmf of this discreet probability distribution is nothing but the random variable, and α is the parameter.

This type of discreet probability distribution is mainly applicable in cases where one wants to find the number of faulty blades in a packet of one hundred blades, or one wants to determine the number of suicides reported in a particular city, etc. The population of the analysis acquires this type of discreet probability distribution and can be used in cases where one wants to determine things such as the number of printing mistakes on each page of a book, the number of cars passing a crossing during the busy hours of a day, the number of airplane accidents in some unit of time, the emission of radioactive (alpha) particles, etc.

The discreet probability distribution, called geometric distribution, has the probability mass function (pmf) that is given by the following:

P(X=x)=qx p; x=0,1, …..

This discreet probability distribution is generally applicable in cases that consist of a series of independent trials, and where the probability of success, which is represented by ‘p,’ is generally constant.

The discreet probability distribution, called hyper geometric distribution, has the probability mass function (pmf) which is given as the following:

P(X=x)= Mck N-Mcn-k / Ncn ; k= 0 , 1 , ….. , min(n,M).

The pmf of this discreet probability distribution consists of the parameters namely ‘N,’ ‘M,’ and ‘n,’ and these parameters are positive integers. This discreet probability distribution is applicable in experiments such as an experiment where the drawing of balls by means of simple random sampling is done without the replacement.

The discreet probability distribution, called multinomial distribution, is basically nothing but the generalization of the binomial distribution whose probability mass function (pmf) is given by the following:

p(x1, x2, …. , xk)=(n!/ x1!, x2!, …. , xk!) p1x1, p2x2, ….. , pkxk , ∑xi = n and ∑pi=1, i=1, .. , n.

This type of discreet probability distribution is applicable in those kinds of experiments where there is the ‘n’ repeated trials in which each number of trials has the possibility of having a discreet number of outcomes.