Background A quick calculation yields, E[Mn]u,var(Mn)= n The variance of M decreases to zero as n increases. Thus the bulk of the distribution of Mm must be very close to the mean u. This phenomenon is the subject of certain laws of large numbersBackground ◼ A quick calculation yields, 𝐄[𝑀𝑛] = 𝜇, var(𝑀𝑛) = 𝜎 2 𝑛 . ◼ The variance of 𝑀𝑛 decreases to zero as 𝑛 increases. ◼ Thus the bulk of the distribution of 𝑀𝑛 must be very close to the mean 𝜇. ◼ This phenomenon is the subject of certain laws of large numbers