 signal. It is interesting to see what a succession of such sampling measurements looks like in the real world. Figure 2.7 shows the plot of a series of 200 samplings of a random variable x following a Gaussian distribution with <x> = 0 and o = 0.1, as generated by a computer program. We observe that, as expected, the values of x are randomly distributed above and below the X axis. The sampling points form a cloud that is denser near the axis, defining a region of width 20. The figure also includes the corresponding plot of x2, which shows that most of the sampling points are found between x2 = 0 and x2 = <x2. > = O. It is important to distinguish the discrete sampling points (here numbering 200) from the continuous, Gaussian PDF. To compare the two, we can draw a histogram of the sampling points, as shown in Fig. 2.8. The histogram represents the counts of points corresponding to the different values of X in Fig. 2.7. For clarity, I have multiplied the sampled variable x by a hundredfold and truncated the result (y = 100x) to an integer, which gives values ranging from y = -23 to y = +29. As seen from Fig. 2.8, the envelope of the histogram is quite different from that of the actual Gaussian distribution, also plotted in the figure for comparison (with Oy = 100 X Ox = 10). The reason for this discrepancy is twofold. First, once gathered into a histogram, the discrete samplings do not have a sufficient number (here 200) to reproduce the smooth and continuous features of the Gaussian PDF. Second, the data were arbitrarily arranged into truncated integer bins, which enhances the discontinuity of the histogram's envelope. To show how this truncation changes the envelope, a second histogram was made with Z = 50x (see inset in Fig. 2.8). This second histogram has a smoother envelope, because there are more data in each of the integer bins. For this 2.4 Uniform, exponential, and Gaussian distributions Figure 2.7 Example of discrete samplings (200 events) of a Gaussian distribution (<x> = 0, o = 0.1), showing the outcom