Central limit theorem The distribution of the sum of a large number of independent identically distributed random variables is approximately Gaussia" When the random errors in measurements are made up of many small contributing random errors, their sum will be gaussian Any linear operation on Gaussian distribution will generate another Gaussian. Not the case for other distributions which are derived by convolving the two density functions 03/1203 12540Lec10 Summary Examined simple least squares and weighted least squares Examined probability distributions Next we pose estimation in a statistical frame ork03/12/03 12.540 Lec 10 21 Central Limit Theorem • • “The distribution of the sum of a large number of is approximately Gaussian” • When the random errors in measurements are made up of many small contributing random errors, their sum will be Gaussian. • generate another Gaussian. Not the case for other density functions. Why is Gaussian distribution so common? independent, identically distributed random variables Any linear operation on Gaussian distribution will distributions which are derived by convolving the two 03/12/03 12.540 Lec 10 22 work Summary • Examined simple least squares and weighted least squares • Examined probability distributions • Next we pose estimation in a statistical frame 11