Generalized Binomial

   In generalized binomial, a binomial distribution is well known as probability distribution. It defined as the probabilities related with the number of possibilities in an experiment .In generalized binomial an outcomes are denoted as a binomial distribution.An experiment and its results give grow to an individual probability distribution known as the binomial distribution.

 

Generalized binomial:

 

Let us see about Characteristics of a generalized binomial:

  • In generalized binomial an experiment deal with continuous trials.
  • Every trial containing two possible answers such as success or a failure.
  • The probability which having an exacting outcome will happen on several given trial is stable.
  • Every one present in trials with this experiment is known as an independent.

 

 Properties of the generalized binomial:

Let us see about the properties of generalized binomial,

  • The mean of the distribution (μx) is calculated by, n * P .
  • The variance (σ2x) is calculated by, n * P * ( 1 - P ).
  • Standard deviation σ is calculated by, √npq

 

 

Examples:

 

1) Consider a coin is tossing six times. Determine the mean, variance and standard deviation while the number of heads that will be presented using generalized binomial.

Solution:

    With the formulas for the binomial distribution and n = 6, p = 1/2, and q = 1/2, the results are

Mean ,µ =n * P = 6 *.5 = 3

Variance, σ2x = n * P * (1 - P). = 6* .5* .5 = 1.5

Standard deviation σx =√npq = √1.5 = 1.22.

2) consider a coin is tossed four times. Determine the mean, variance and standard deviation while the number of tails that will be presented using generalized binomial.

Solution:

From the formulas to the binomial distribution and n = 4, p = 1/2, and q = 1/2, the results are

Mean, µ =n * P = 4 *.5 = 2

Variance ,σ2x = n * P * ( 1 - P ) = 4* .5* .5 = 1

Standard deviation σx =√npq = √4*.5*.5 = 1