#a) 
pbinom(3,30,0.12) #distr. fce
sum(dbinom(0:3,30,0.12))

#b)
1-pbinom(2,30,0.12)
1-sum(dbinom(0:2,30,0.12))

#c)
dbinom(3,30,0.12)

#d)
sum(dbinom(2:5,30,0.12))

x<-seq(0,15)
dens<-dbinom(x,30,0.12)
distr<-pbinom(x,30,0.12)
n<-length(x)

#pstni fce
plot(x,dens,type='h',,main='Pravdepodobnostni funkce - pojistne udalosti',xlab='pocet pojistnych udalosti',
     ylab='pravdepodobnostni funkce')
points(x,dens,col='red',pch=19)

#distr fce
plot(x,distr,type='n',xlim=c(-1,17),ylim=c(0,1),main='Distribucni funce - pojistne udalosti',
     xlab='pocet pojistnych udalosti',
     ylab='distribucni fce')
segments(x,distr,x+1,distr)
points(x,distr,col='red',pch=19)
points(x[1:n]+1,distr[1:n],pch=21, col='red', bg='white')
points(x+1,distr,pch=21,col='red',bg='white')
points(0,0,pch=21,col='red', bg='white')

arrows(16,1,17,1,length=0.15)
arrows(x[1],0,-1,0,length=0.15)