X<-read.table("C:/Users/Marija/Desktop/OPS/oldFaithful.txt")
x<-X$V1
n<-length(x)
par(mfrow=c(2,2))
hist(x, xlim=c(0,6))
#histogram po Sturdzisovom pravilu
broj<-ceiling(1+log2(n)) #ceo deo + 1 
sirina<-diff(range(x)/broj)
breaks<-min(x)+sirina*0:broj
hist(x, breaks=breaks, xlim = c(0,6))

h<-0.25
K<-function(t){
  if(abs(t)<1)
    return(1/2)
  else
    return(0)
}
y<-seq(1,6,0.01) #tacke u kojima se racuna gustina
fo<-c()
for(j in 1:length(y)){
  suma<-0
  for(i in 1:n){
    suma<-suma+K((y[j]-x[i])/h)
    fo[j]<-1/(n*h)*suma
  }
}
plot(y,fo,type="l")