n <- 200

u <- runif(n)

u

hist(u)

mean(u)

z <- sqrt(n)*(mean(u) - 0.5)/sqrt(1/12)
z


var(u)

y <- sum(u < 0.1)
y <- c(y,sum(u < 0.2) - sum(u < 0.1))
y <- c(y,sum(u < 0.3) - sum(u < 0.2))
y <- c(y,sum(u < 0.4) - sum(u < 0.3))
y <- c(y,sum(u < 0.5) - sum(u < 0.4))
y <- c(y,sum(u < 0.6) - sum(u < 0.5))
y <- c(y,sum(u < 0.7) - sum(u < 0.6))
y <- c(y,sum(u < 0.8) - sum(u < 0.7))
y <- c(y,sum(u < 0.9) - sum(u < 0.8))
y <- c(y,sum(u < 1.0) - sum(u < 0.9))

chisq.test(y,p = rep(1/length(y), length(y)))

plot.ecdf(u)

lines(c(0,1),c(0,1))

ks.test(u, "punif" )

ks.order <- order(seq(1:n)/n - sort(u))

ks.order[1]
ks.order[1]/n - sort(u)[ks.order[1]]

ks.order[n]
ks.order[n]/n - sort(u)[ks.order[n]]

plot(u[1:n-1],u[2:n])
plot(u[1:(n-2)],u[3:n])

acf(u)