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and similarly across the spectrum of variabilities. Therefore, standardization is called for. The variables were standardized and the Z-vectors found, Z i = (X i i ) / ii , using the means and standard deviations from Figure 1.1. Note that normality of the data is not strictly required to perform noninferential PCA [4] but that departures from normality may diminish the correlations observed [5]. Since we do not plan to perform inference based on our PCA, we will not worry about normality at this time. In s 2 and 3 we discuss methods for transforming nonnormal data. Next, we examine the matrix plot of the predictors in Figure 1.3 to explore whether correlations exist. Diagonally from left to right, we have the standardized variables minc-z (median income), hage-z (housing median age), rooms-z (total rooms), bedrms-z (total bedrooms), popn-z (population), hhlds-z (number of households), lat-z (latitude), and long-z (longitude). What does the matrix plot tell us about the correlation among the variables Rooms, bedrooms, population, and households all appear to be positively correlated. Latitude and longitude appear to be negatively correlated. (What does the plot of latitude versus longitude look like Did you say the state of California ) Which variable appears to be correlated the least with the other predictors Probably housing median age. Table 1.1 shows the correlation matrix for the predictors. Note that the matrix is symmetrical and that the diagonal elements all equal 1. A matrix plot and the correlation matrix are two ways of looking at the

There is no username and password combination on either the web interface or the Telnet interface. You can enable a password on the Telnet configuration interface or disable the Telnet interface entirely. This doesn t affect the web interface, which has no password protection, but you can also disable that interface too.

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Remark If the Markov chain is irreducible and aperiodic, it has a unique stationary distribution on the states, and any initial distribution tends to the stationary distribution as n . In this case, even though the initial distribution is not the stationary distribution, the entropy rate, which is de ned in terms of long-term behavior, is H (X), as de ned in (4.25) and (4.27). 4.3 EXAMPLE: ENTROPY RATE OF A RANDOM WALK ON A WEIGHTED GRAPH As an example of a stochastic process, let us consider a random walk on a connected graph (Figure 4.2). Consider a graph with m nodes labeled {1, 2, . . . , m}, with weight Wij 0 on the edge joining node i to node j . (The graph is assumed to be undirected, so that Wij = Wj i . We set Wij = 0 if there is no edge joining nodes i and j .) A particle walks randomly from node to node in this graph. The random walk {Xn }, Xn {1, 2, . . . , m}, is a sequence of vertices of the graph. Given Xn = i, the next vertex j is chosen from among the nodes connected to node i with a probability proportional to the weight of the edge connecting i to j . Thus, Pij = Wij / k Wik .

dispersed conductive and nonconductive particles, laminated between electrodes. The laminate is transformed into a surge protection device using process similar to that used for manufacturing PCBs. The overall thickness of the PVS device is in the range less than 10 mils. The PVS material does not require a substrate and consequently, the trigger voltage of the device is set by device dimensions and the polymer formula. These components allow for single- or multiple-array surface mount components and connector arrays. Installing the protection array on the connector itself provides ESD protection at the input traces of ESD sensitive components and semiconductors. Shrier et al. [9] demonstrated PVS elements with approximately 100 fF loading capacitance. Polymer voltage suppression elements were achieved with less than 200 ps rise times and effective clamping time of less than 10 ns [9,10]. Figure 10.5 shows an example of a ESD failure in a cell phone application. Today, gallium arsenide power ampli ers are used in cell phone applications because of the high Johnson Limit of GaAs technology. ESD failure is evident in the passive elements on the cell phone prototype application. ESD damage occurred in a resistor element. Figure 10.6 shows the integration of the PVS devices on the board of the cell phone application. ESD protection is provided off-chip (e.g., on the board) instead of a on-chip GaAs semiconductor chip.