######################
##  Harjoitukset 4  ##
######################


#########
## 4.4 ##
#########

x<-c(1.02,1.41,1.75,2.31,3.42,4.31,9.21,17.4,38.6,392.8)
n<-10
theta<-n/sum(log(x))
a<-n*log(theta)-(theta+1)*sum(log(x))+log(0.1)+sum(log(x))
b<-sum(log(x))
fn<-function(theta){n*log(theta)-b*theta-a}

curve(fn(x),0,1.5, lwd=2,xlab=expression(theta),main="tehtava 4.4")
abline(h=0)
abline(v=0.243)
abline(v=0.961)

#lines(c(0,1.5),c(0,0))
#lines(c(0.243,0.243),c(-25,5))
#lines(c(0.961,0.961),c(-25,5))

uniroot(fn,c(0.1,0.4))
#$root
#[1] 0.2429697
#
#$f.root
#[1] -0.0001355576
#
#$iter
#[1] 6
#
#$estim.prec
#[1] 6.103516e-05

uniroot(fn,c(0.7,1))
#$root
#[1] 0.9606551
#
#$f.root
#[1] -7.668373e-07
#
#$iter
#[1] 4
#
#$estim.prec
#[1] 6.103516e-05