them being convenient to work with the central limit theorem classical CLT says that let x1 x2 be an infinite sequence of independent random variables with an expected values mu and variance Sigma squared then we define a new variable ZM Zn is the sum of all of them minus the sum of the averages so this should be centered around 0 because the sum of all the mind is the sum of the averages or expectations and then normalize by this quantity over here it's a scale down then for the limit of n going to infinity with