This article gives two concrete illustrations of the central limit theorem. Both involve the sum of independent and identically-distributed random variables and show how the probability distribution of the sum approaches the normal distribution as the number of terms in the sum increases. The first illustration involves a continuous probability distribution, for which the random variables have a probability density function. The second illustration, for which most of the computation can be done by hand, involves a discrete probability distribution, which is characterized by a probability mass function. A free full-featured interactive simulation that allows the user to set up various distributions and adjust the sampling parameters is available through the External links section at the bottom of this page.