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# Binomial distribution in R

We have one experiment with two possible results (success and fail) where the probability of success is Π. In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments.

If we repeat independent trials in the same conditions the variable…

x = number of success in n trails

follow a binomial distribution of n parameters and Π, and we write X ∈ Bin (n, Π). We can calculate mean and standard deviation too. The function dbinom in R calculate the odds of one variable follow binomial distribution. We can use..

dbinom(x, size, prob, log = FALSE)
pbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)
qbinom(p, size, prob, lower.tail = TRUE, log.p = FALSE)
rbinom(n, size, prob)

We show this with an example in R.

n=8
prob=0.15
x=0:n
p=dbinom(x, size=n, prob=prob)
# p1=round(p,4)
names(p)=x
r=barplot(p,col=’grey85′,ylim=c(0,0.45),
main=paste(“Bin(n=8,p=”,prob,”)”,sep=””))
text(r,p,round(p,2),pos=3,cex=0.7)

## Showing binomial datas in R

We get the Fig. 1 for one probability of 0.15, Fig. 2 for 0.25, Fig 3. for 0.50, Fig 4. for 0.75.