# a)
pbinom(6,30,0.12)
# b)
1-pbinom(5,30,0.12)
# c)
dbinom(6,30,0.12)
# d)
sum(dbinom(2:5,30,0.12))

x<-seq(0,30)
dens<-dbinom(x,30,0.12)
n<-length(x)

plot(x,dens,type='n',xlab='pocet pojistnych udalosti zpusobenych vloupanim',
     ylab='pravdepodobnost',main='Binomicke rozlozeni - pstni fce',
     pch=19,lwd=2,col='red')
for(i in 1:n){
  lines(c(x[i],x[i]),c(0,dens[i]))}
points(x,dens,col='red',pch=19)

#----------------------------------------------------------
distr<-pbinom(x,30,0.12)
plot(x,distr,type='n',xlab='pocet pojistnych udalosti zpusobenych vloupanim',
     ylab='distribucni fce',main='Binomicke rozlozeni - distr.fce',
     pch=19,lwd=2,xlim=c(0,30))
for(i in 1:n){
  lines(c(x[i],x[i+1]),c(distr[i],distr[i]))}
points(x[2:30],distr[2:30],pch=19,col='red')
points(x[2:30],distr[1:29],pch=19,col='white')
points(x[2:30],distr[1:29],pch=1,col='red')
arrows(x[30],distr[30],x[30]+1,distr[30],length=0.15)
arrows(x[2],distr[1],-0.1,distr[1],length=0.15)