function (pdf = F) 
{
    if (pdf == T) 
        pdf("clt3.pdf", width = 9, height = 6)
    par(mfrow = c(3, 2))
    n = 10000
    alpha = 1
    beta = 2
    mu = -2
    x1 = rnorm(n)
    x2 = runif(n)
    x3 = exp(rnorm(n) + mu)
    x4 = alpha * (-log(1 - runif(n)))^(1/beta)
    x5 = alpha * (-log(1 - runif(n)))^(1/beta)
    hist(x1, main = "standard normal population", prob = T, ylim = c(0, 
        0.5), nclass = 50, xlab = expression(x[1]))
    t = (0:60)/10 - 3
    yt = exp(-t^2/2)/sqrt(2 * pi)
    lines(t, yt)
    hist(x2, main = "uniform population on (0,1)", prob = T, 
        ylim = c(0, 1.3), nclass = 50, xlab = expression(x[2]))
    segments(0, 0, 0, 1)
    segments(0, 1, 1, 1)
    segments(1, 1, 1, 0)
    hist(x3, main = "a log-normal population", prob = T, ylim = c(0, 
        5), nclass = 200, xlim = c(0, 1.5), xlab = expression(x[3]))
    lines(exp(t + mu), yt/exp(t + mu))
    hist(x4, main = "Weibull population", prob = T, nclass = 50, 
        xlab = expression(x[4]))
    t = (0:300)/100
    yt = (t/alpha)^(beta - 1) * exp(-(t/alpha)^beta) * beta/alpha
    lines(t, yt)
    hist(x5, main = "Weibull population", prob = T, nclass = 50, 
        xlab = expression(x[5]))
    t = (0:300)/100
    yt = (t/alpha)^(beta - 1) * exp(-(t/alpha)^beta) * beta/alpha
    lines(t, yt)
    if (pdf == T) {
        dev.off()
        pdf("clt4.pdf", width = 9, height = 6)
    }
    readline("hit return\n")
    par(mfrow = c(2, 1))
    xsum = x1 + x2 + x3 + x4
    m = mean(xsum)
    s = sqrt(var(xsum))
    hist(xsum, main = "Central Limit Theorem at Work", prob = T, 
        nclass = 50, xlab = expression(x[1] + x[2] + x[3] + x[4]))
    t = ((0:60)/10 - 3) * s + m
    ty = exp(-(t - m)^2/(2 * s^2))/(sqrt(2 * pi) * s)
    lines(t, ty)
    xsum = x2 + x3 + x4 + x5
    m = mean(xsum)
    s = sqrt(var(xsum))
    hist(xsum, main = "Central Limit Theorem at Work", prob = T, 
        nclass = 50, xlab = expression(x[2] + x[3] + x[4] + x[5]))
    t = ((0:60)/10 - 3) * s + m
    ty = exp(-(t - m)^2/(2 * s^2))/(sqrt(2 * pi) * s)
    lines(t, ty)
    if (pdf == T) 
        dev.off()
}