#6.1
qnorm(0.5)
qnorm(0.25)
qnorm(0.75)

#6.2
qnorm(0.25, 3, sqrt(5))

#6.3
qchisq(0.025, 25)

#6.4
qt(0.99, 30)
qt(0.05, 14)

#6.5
qf(0.975, 5, 20)
qf(0.05, 2, 10)

#6.6 - Hod kostkou 
x <- 1:6
px <- rep(1/6, 6)
(EX <- sum(x*px))
(DX <- sum(x^2*px) - EX^2) # DX = E(X^2)-(EX)^2

# 6.8 - Pohrebni ritual
x <- c(1, 2)
y <- c(3, 4)
pi <- data.frame(N3=c(0.1, 0.35), N4=c(0.3, 0.25),
                 row.names=c('R1', 'R2'))

px <- apply(pi, 1, sum)
py <- apply(pi, 2, sum)
EX <- sum(x*px)
EY <- sum(y*py)
DX <- sum(x^2*px)-EX^2
DY <- sum(y^2*py)-EY^2
CXY <- (x[1]-EX)*(y[1]-EY)*pi[1,1]+
        (x[1]-EX)*(y[2]-EY)*pi[1,2]+
        (x[2]-EX)*(y[1]-EY)*pi[2,1]+
        (x[2]-EX)*(y[2]-EY)*pi[2,2]
RXY <- CXY/(sqrt(DX)*sqrt(DY))
RXY

# 6.13 - Elektrospotrebice
1-pbinom(96,400,0.2)
1-pnorm(96, 80, 8)