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The median cost will lie between the expected cost and the most likely value of total cost The 2% difference between the expected value of 102 and the most likely value of 100 is negligible, but it is small only because of the nearly symmetric shape of these distributions For completely symmetric distributions, this difference would be zero If 8 were the most likely value, with a probability of 05, while 10 and 12 had probabilities of 03 and 02, respectively, the expected value would be (8 05) (10 03) (12 02) 94 With this skewed distribution the difference between the most likely value and the expected value is substantial, some 18% of the most likely value Such a difference in magnitudes is common, arising from much less extreme asymmetry but much longer distribution tails .

lemon (or football) shape. If the tube radius is larger than the torus radius, you create a puckered ball (or apple) shape. (You cannot get such unusual shapes using the Torus shape on the Surfaces toolbar.)

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We wanted to include a chapter on Options because they are yet another weapon that can be included in one s trading arsenal. Options are confusing to most traders and, therefore, are overlooked. Len Yates, with his expertise, clears up the confusion and introduces several option strategies. The ideas that are presented can be used with most option analysis software. Being from the Chicago area, host to some of the world s largest options exchanges, I know or encounter many people whose work is related to options trading. So I have the advantage of being surrounded by plenty of locals who are familiar with options and how they work. Still, there are likely even more people unfamiliar with options. During the course of many social engagements, I invariably end up leading a discussion on options and what options are. Without even finishing my standard overview, I am invariably met with a response such as, Well, that sounds too complicated for me from a befuddled listener. This usually leads me to the snack table because I don t want to make any party listen to what might be to them an arcane subject. But what I want to say, and sometimes do, is that options are not really that complicated if you re committed to learning the terminology and the basic principles of the game. I like comparing options to chess: if you spend an hour learning the rules, you may find you like the game and can win at it, too.

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Description Rotates multiple text, Mtext, and attribute definitions to a specified angle without moving them, or aligns them so that they re horizontal or right-side up for easy reading. Encloses selected Text or Mtext inside a circle, a slot (a rectangle, but with arcs at each end), or a rectangle. Numbers lines of text by adding a prefix or suffix, or by overwriting the text. Offers the following ways to change the case of text: uppercase, lowercase, sentence case, title case, and toggle case.

zero crossing. In other words, cause and effect happen at the same frequency and with only a time delay between them. What is different between output and input is the frequency; the output frequency being lower by the divide ratio, N . The frequency is divided by N uniformly so frequency deviation f is also divided by N . Thus the FM modulation index, mFM = is smaller by a factor N at the output, mFMo = mFMi /N. (8.14) f , fm (8.13)

Looked at some of PHP s drawing functions, including imagesetpixel(), imageline(), imagerectangle(), imageellipse(), imagearc(), and imagepolygon() Saw how to open existing images with imagecreatefromjpeg(), imagecreatefromgif(), and imagecreatefrompng() so that you can manipulate them. By way of example, you applied a watermark image to an existing photograph, and created a thumbnail image based on an existing image. Along the way you looked at the concepts of transparency and opacity Added text to an image using imagestring() and imagefttext()

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