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**Example text**

01. = The t-test requires the original random variables to be Gaussian. When they are not, we can resort to the Central Limit Theorem and use the test asymptotically. We take n batches of m random vari"bles xi j ), X~j), ... , xg) for j = 1,2, ... ) with mean fJ, and variance ()2. A~) and the sample 34 CHAPTER 1. BACKGROUND FROM PROBABILITY variances (o-g»)2 for each batch j = 1,2, ... ,n and use the Central Limit Theorem to conclude that the Ag) are approximately Gaussian. The preceding t-test is then approximately valid for these batch averages (rather than for the original xij»).

Repeat the calculations for a person originally living in district W. 6. PW); UNTIL K=2; 45 46 CHAPTER 1. 1 (i) Only the core of the program is listed here. 8) below. (ii) Of course, better results will be possible' for larger values of M and N, but will require considerably more computational time. (iii) The procedure SETTABLETOSCR prepares a table on the screen, into which the results are inserted by the procedure SETDATATOSCR as they are calculated. 8) a stationary probability vector for the homogeneous Markov chain.

Say n = 10 3 , generate n realizations of Yn . 05 to obtain an indication of the graph of the density function of Y n . Then estimate the mean-square error E(IYn - X12) for a larger n, say n = 104 • Does this suggest that Y n converges to X in the mean-squnre sense? 4. 1 (i) The Gaussian random numbers are provided by the Polar Marsaglia generator GENERATE. (ii) For information about. 3. (iii) The procedure SETTABLETOSCR is used in a slightly different way here, now providing the estimated mean-square error.