Background It can be seen that E[Zn]=0, var[Zn]1 Since the mean/variance of Zm remain unchanged as n increases,its distribution neither spreads,nor shrinks to a point. The central limit theorem is concerned with 0 the asymptotic shape of the distribution of Zn and asserts that Z,becomes the standard normal distribution.Background ◼ It can be seen that 𝐄 𝑍𝑛 = 0, var 𝑍𝑛 = 1 ◼ Since the mean/variance of 𝑍𝑛 remain unchanged as 𝑛 increases, its distribution neither spreads, nor shrinks to a point. ◼ The central limit theorem is concerned with ❑ the asymptotic shape of the distribution of 𝑍𝑛 ❑ and asserts that 𝑍𝑛 becomes the standard normal distribution