#gaussisk
liste = c(29.59, 29.23, 31.05, 17.43, 31.27, 23.79, 36.49, 40.09)
#posterior hyperparametere
k0 = 0
S0 = 0
C0 = 0
n = 8 #viktig faktor
k1 = k0 + n
k1 #k1 verdi
S1 = S0 + sum(liste)
S1
C1 = C0 + sum(liste^2)
C1
v1 = -1 + n
m = S1/k1 #mean
SS1 = C1 - k1 * m^2
SS1
s1 = sqrt(SS1/v1)
#posterior values
#tau
xVals = seq(0,0.1,0.001)
yVals = dgamma(xVals,v1/2,SS1/2)
plot(xVals,yVals,type = "l", col = "red")
#forventet
xVals1 = seq(0,50,0.01)
yVals1 = dt.scaled(xVals1, v1 , m , s1 * sqrt(1/k1))
plot(xVals1, yVals1 , type = "l", col = "blue")
s1 * sqrt(1/k1)
#prediktiv
xVals2 = seq(0,50,0.01)
yVals2 = dt.scaled(xVals1, v1 , m , s1 * sqrt(1+1/k1))
plot(xVals1, yVals2 , type = "l", col = "blue")
s1 * sqrt(1+1/k1)
#II P(X+ < 18 ) #oppgavene varier
pt.scaled(18, v1 , m , s1 * sqrt(1+1/k1))
# P(X+ < 18 ) = 0.0772085
#III svarveien #oppgavenen varierer #gjort noe feil
sd = sd(liste)
sd
m = m
m
#putter tallene i normalfordelingen
yVals4 = dnorm(xVals2, m , sd)
plot(xVals2,yVals4,type = "l", col = "green", main = "Snarvei(normal) er grønn og X+ er rød")
lines(xVals2, yVals2,type = "l", col = "red")
# ingen kommentar
#IV #hypotesetest referanse punkt
# H1: X+ > 18
# H0 : ≤ X+ 18
pt.scaled(18,v1,m,s1 * sqrt(1+1/k1))
# 0.0772 > 0.05
#forkaster ikke H0 i fordel for H1
#Normalfordeling
pnorm(18,m,sd)
# 0.04519901 < 0.05
#forkaster H0 til fordel for H1