# Gauss/normalis eloszlas
# alapert: standard, mean = ve = 0, sd = szoras = 1
x <- seq(-3,3,0.1)
# eloszlasfuggveny
plot(x,pnorm(x),type="l")
# surusegfuggveny: haranggorbe
lines(x,dnorm(x),col="blue")
# kvantilis = ?
# q-kvantilis: x szam, aminel a val valt. q esellyel kisebb vagy egyenlo
# 0.7-kvantilis: mi az az x, aminel 0.7 esellyel kisebb a standard Gauss?
abline(h=0.7,lty=2)
qnorm(0.7)
abline(v=qnorm(0.7),lty=2)

# 2. abra, futtassuk kulon innentol!
# kvantlis-fuggveny, mint az eo-fv inverze:
x <- seq(-2,2,0.1)
# eloszlasfuggveny
plot(x,pnorm(x),type="l",ylim=c(-2,2))
# kvantilis-fuggveny
z <- seq(0,1,0.05)
lines(z,qnorm(z),col="blue")
abline(0,1,lty=2)
q2 <- c(0.25,0.5,0.75)
points(q2,qnorm(q2),pch=1:3,col="blue")
points(qnorm(q2),q2,pch=1:3,col="red")