##################################
####oppgave 6          
##################################

# Leser inn dataene fra tabell 13.2:
N=c(195,73,100)

# Sannsynligheter under nullhypotesen om Mendelsk nedarving:
p0=c(9/16,3/16,4/16)

# Forventete antall:
n=sum(N)
E=n*p0

# Tabell over observerte og forventete antall:
rbind(N,E)

# Kji-kvadrat observator:
X2=sum((N-E)^2/E)

# Vi kan bruke kommandoen "chisq.test" til ? gj?re beregningene:
X2test=chisq.test(N,p=p0)
X2test
rbind(X2test$observed,X2test$expected)



##################################
#### oppgave 8
##################################

# Leser inn dataene fra tabell 13.2:
N=c(11, 24, 69, 96)

# Sannsynligheter under nullhypotesen om Mendelsk nedarving:
p0=c(7/365,(30-8+1)/365,(90-31+1)/365,(365-91+1)/365)

# Forventete antall:
n=sum(N)
E=n*p0

# Tabell over observerte og forventete antall:
rbind(N,E)

# Kji-kvadrat observator:
X2=sum((N-E)^2/E)

# Vi kan bruke kommandoen "chisq.test" til ? gj?re beregningene:
X2test=chisq.test(N,p=p0)
X2test
rbind(X2test$observed,X2test$expected)



##################################
####oppgave 9 b          
##################################

obs <-  c(.10, .99, 1.14, 1.26, 3.24, .12, .26, .8, .79, 1.16, 1.76, .41, .59, .27, 2.22, .66, .71, 2.21, .68, .43, .11, .46, .69, .38, .91, .55, .81, 2.51, 2.77, .16, 1.11, .02, 2.13, .19, 1.21, 1.13, 2.93, 2.14, .34, .44)
n = sum(obs)

#intervallgrenser dersom det skal v?re like sannsynlig ? havne i alle intervallene. 
a <- c(0, .223, .510, .916, 1.609, Inf)

N <- c() ; p0<-c()
k <- 5
temp <- sort(obs)
for(i in 1:k){
	gr 		<- which(temp < a[i+1])
	N[i] 	<- length(gr)
	temp 	<- temp[-gr]
	p0[i] 	<- exp(-a[i]) - exp(-a[i+1])			#n?rme 1/5
}

E = n*p0
rbind(N,E)
chitest = sum((N-E)^2/E)
chiAlpha = qchisq(0.1,k-1, lower.tail=FALSE)
Pvalue = 1-pchisq(chitest,k-1)
paste("Chisq=",round(chitest, 2), ", ChiAlpha=", round(chiAlpha, 2), ", P-value=",round(Pvalue,2))


##################################
####oppgave 13
##################################

N = c(1212, 118, 58)
k = length(N)
n = sum(N)

#finner theta.hat ved ? derivere likelihooden:
theta.hat <- (N[2]+2*N[3])/(2*sum(N))			#0.084

p.hat = c((theta.hat-1)^2,(1 - theta.hat)*theta.hat*2, theta.hat^2 )
m=length(theta.hat)
E = n*p.hat
show(rbind(N,E))
chitest = sum((N-E)^2/E)
chiAlpha = qchisq(0.05,k-1-m, lower.tail=FALSE)
Pvalue = 1-pchisq(chitest,k-1-m)
paste("Chisq=",chitest, ", ChiAlpha=", round(chiAlpha, 3), ", P-value=",round(Pvalue,3))