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If we draw an object from an urn, we have the choice of replacing or not replacing the object into the urn before we draw again. In the first case a particular object can come up again and again, whereas in the second it can come up only once. Sampling where each member of a population may be chosen more than once is called sampling with replacement, while sampling where each member cannot be chosen more than once is called sampling without replacement. A finite population that is sampled with replacement can theoretically be considered infinite since samples of any size can be drawn without exhausting the population. For most practical purposes, sampling from a finite population that is very large can be considered as sampling from an infinite population.

For the ac steady state where s j!, we have Z1 j!L1 The re ected impedance is Zreflected M 2 !2 Z2 j!L2 19 18

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Clearly, the reliability of conclusions drawn concerning a population depends on whether the sample is properly chosen so as to represent the population sufficiently well, and one of the important problems of statistical inference is just how to choose a sample. One way to do this for finite populations is to make sure that each member of the population has the same chance of being in the sample, which is then often called a random sample. Random sampling can be accomplished for relatively small populations by drawing lots or, equivalently, by using a table of random numbers (Appendix H) specially constructed for such purposes. See Problem 5.43. Because inference from sample to population cannot be certain, we must use the language of probability in any statement of conclusions.

The load Z2 is seen by the source as M 2 !2 = Z2 j!L2 . The technique is often used to change an impedance to a certain value; for example, to match a load to a source.

A population is considered to be known when we know the probability distribution f (x) (probability function or density function) of the associated random variable X. For instance, in Example 5.1 if X is a random variable whose values are the heights (or weights) of the 12,000 students, then X has a probability distribution f (x). If, for example, X is normally distributed, we say that the population is normally distributed or that we have a normal population. Similarly, if X is binomially distributed, we say that the population is binomially distributed or that we have a binomial population. There will be certain quantities that appear in f (x), such as and in the case of the normal distribution or p in the case of the binomial distribution. Other quantities such as the median, moments, and skewness can then be determined in terms of these. All such quantities are often called population parameters. When we are given the population so that we know f (x), then the population parameters are also known. An important problem arises when the probability distribution f(x) of the population is not known precisely, although we may have some idea of, or at least be able to make some hypothesis concerning, the general behavior of f(x). For example, we may have some reason to suppose that a particular population is normally distributed. In that case we may not know one or both of the values and and so we might wish to draw statistical inferences about them.

Calculate the functional cohesion measures for the following code fragment. cin >> a >> b; int x,y,z; x=0; y=1; z=1; if (a > b){ x = a*b; while (10 > a){ y=y+z; a=a+5; } else { x=x+b; } Fig. 9-7 shows each token from the code. The arcs are drawn from each token to all tokens that are immediately affected by the value of that token.

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