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.
Properties of the generalized binomial:
Let us see about the properties of generalized binomial,
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, σ^{2}_{x =} n * P * (1 - P). = 6* .5* .5 = 1.5
Standard deviation σ_{x} =√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 ,σ^{2}_{x =} n * P * ( 1 - P ) = 4* .5* .5 = 1
Standard deviation σ_{x} =√npq = √4*.5*.5 = 1