######################
##  Harjoitukset 8  ##
######################


#########
## 8.3 ##
#########

x<-94
n<-200
a<-x*log(x/n)+(n-x)*log(1-x/n)-3.841/2
fn<-function(theta){x*log(theta)+(n-x)*log(1-theta)-a}

curve(fn(x),0,1, lwd=2,xlab=expression(theta),main="tehtava 8.3")
abline(h=0)
abline(v=0.4)
abline(v=0.539)

uniroot(fn,c(0.3,0.5))

# $root
# [1] 0.4015732
#
# $f.root
# [1] 0.001555483
#
# $iter
# [1] 6
# 
# $estim.prec
# [1] 6.103516e-05

uniroot(fn,c(0.5,0.6))

# $root
# [1] 0.5392163
#
# $f.root
# [1] 8.841595e-05
#
# $iter
# [1] 5
# 
# $estim.prec
# [1] 8.836205e-05