A number of results in statistical theory concerning the limiting distribution, under certain conditions, of the (properly scaled) sample average of random variables or random vectors, as the sample size increases to infinity. For example, the Lindeberg–Lévy CLT states that if x₁,…, x_N are independent, identically distributed random vectors with mean vector μ‎ and covariance matrix Σ‎, then $\sqrt{N}\overline{x}$ converges in distribution to a normal random vector with mean μ‎ and covariance matrix Σ‎, where: