qnorm(0.5)
qnorm(0.25)
qnorm(0.75)

qnorm(0.25, 3, sqrt(5))


qchisq(0.025, 25)

qt(0.99, 30)
qt(0.05, 14)

qf(0.975, 5,20)
qf(0.05,  2,10)

#delka bantuske tvare
setwd("~/")
x <- c(67, 67, 63, 68, 70, 70, 75, 74, 80, 77, 77, 67, 64)
x <- sort(x)
n <- length(x)
m <- mean(x)
s2 <- var(x)
s  <- sd(x)
Tab <- data.frame(m=m, s2=s2, s=s, row.names='akcie')
round(Tab, digits=2)

# P(X>=70)
pst <- sum(x>=70)/length(x)
pst2 <- 1-sum(x<70)/length(x)
round(pst,4)
round(pst2,4)

# zavislost delky a sirky lebky
data <- read.delim('16-anova-head.txt', sep='\t')
muzi <- data[data$sex=='m',]
head.w <- muzi$head.W
bizyg.w <- muzi$bizyg.W
cov(head.w, bizyg.w)  # 31.83
cor(head.w, bizyg.w)  # 0.6785
plot(head.w, bizyg.w)


data <- read.delim('16-anova-head.txt', sep='\t')
muzi <- data[data$sex=='m',]
head.w <- muzi$head.W
bizyg.w <- muzi$bizyg.W
bigo.w <- muzi$bigo.W

m <- mean(bigo.w)
s <- sd(bigo.w)
alpha <- 0.05
n <- length(bigo.w)
dh <- m-s/sqrt(m)*qt(1-alpha/2, n-1)
hh <- m-s/sqrt(m)*qt(alpha/2, n-1)

round(dh, 4)
round(hh, 4)

dh <- m-s/sqrt(n)*qt(1-alpha, n-1)
dh

hh <- m-s/sqrt(n)*qt(alpha, n-1)
hh