# Jakaumien kuvaajien piirtäminen
==========================
# Luento 23.11.05
x<-seq(-1,1,0.05)
y<-3*x^2/2
plot(x,y,type="l",col = "red")
x<-seq(0,1,0.05)
y<-3*sqrt(x)/2
lines(x,y)
#================
# Eksponenttijakauma
#================

x<-seq(0,5,0.05)
par(mfrow=c(3,2))
plot(x,dexp(x,1),type="l",ylim=c(0,6))
plot(x,dexp(x,2),type="l",ylim=c(0,6))
plot(x,dexp(x,3),type="l",ylim=c(0,6))
plot(x,dexp(x,4),type="l",ylim=c(0,6))
plot(x,dexp(x,5),type="l",ylim=c(0,6))
plot(x,dexp(x,6),type="l",ylim=c(0,6))

pexp(1,1);pexp(1,2);pexp(1,3);pexp(1,4);pexp(1,5);pexp(1,6);
plot(1:6,c(pexp(1,1),pexp(1,2),pexp(1,3),pexp(1,4),pexp(1,5),pexp(1,6)))
#================
# Gammafunktio
#================
x<-seq(0,5,0.05)
a<-2.5
y<-x^(a-1)*exp(-x)
plot(x,y,type="l",ylim=c(0,2))
a<-3.5
y<-x^(a-1)*exp(-x)
lines(x,y)
a<-4.5
y<-x^(a-1)*exp(-x)
lines(x,y)

# Gammafunktion (integraalin) arvot
gamma(2.5:4.5)

#================
# Gammajakauma
#================

x<-seq(0,5,0.05)
par(mfrow=c(3,2))
plot(x,dgamma(x,1.5,1.5),type="l",ylim=c(0,0.4))
plot(x,dgamma(x,1.5,2.5),type="l",ylim=c(0,0.4))
plot(x,dgamma(x,1.5,3.5),type="l",ylim=c(0,0.4))
plot(x,dgamma(x,2.5,1.5),type="l",ylim=c(0,0.4))
plot(x,dgamma(x,3.5,1.5),type="l",ylim=c(0,0.4))
plot(x,dgamma(x,4.5,1.5),type="l",ylim=c(0,0.4))

# P(2<X<5), kun X~Gamma(1.5,2.5)
pgamma(5,1.5,2.5)-pgamma(2,1.5,2.5)

#=======================
# Khi2-jakauma
#======================
# X~Khi2(r), r>0 (r kokonaisluku),
# kun X~Gamma(r/2,2)

x<-seq(0,5,0.05)
par(mfrow=c(3,2))
plot(x,dchisq(x,1),type="l",ylim=c(0,0.5))
plot(x,dchisq(x,2),type="l",ylim=c(0,0.5))
plot(x,dchisq(x,3),type="l",ylim=c(0,0.5))
plot(x,dchisq(x,4),type="l",ylim=c(0,0.5))
plot(x,dchisq(x,5),type="l",ylim=c(0,0.5))
plot(x,dchisq(x,6),type="l",ylim=c(0,0.5))


#================
# Normaalijakauma
#================

x<-seq(-5,5,0.05)
plot(x,dnorm(x),type="l",ylim=c(0,1),col = "red")
lines(x,dnorm(x,0,0.3));lines(x,dnorm(x,0,0.7));
lines(x,dnorm(x,0,1.5));lines(x,dnorm(x,0,,2));
lines(x,dnorm(x,0,2.5));lines(x,dnorm(x,0,,3));