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487 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
487 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
488 \mode<presentation>{ |
488 \mode<presentation>{ |
489 \begin{frame}[c] |
489 \begin{frame}[c] |
490 \frametitle{Random Number Generators} |
490 \frametitle{Random Number Generators} |
491 |
491 |
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492 \begin{itemize} |
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493 \item Computers are deterministic. How do they generate random numbers?\bigskip\pause |
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494 |
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495 \item The most popular method to generate random numbers between \bl{$0$} and \bl{$m$} is: choose |
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496 three integers |
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497 |
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498 \begin{center} |
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499 \begin{tabular}{ll} |
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500 \bl{$a$} & multiplier\\ |
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501 \bl{$c$} & increment\\ |
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502 \bl{$X_0$} & start value |
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503 \end{tabular} |
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504 \end{center} |
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505 |
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506 and calculate |
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507 |
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508 \begin{center} |
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509 \bl{$X_{n+1} = (a * X_n + c) \;mod\; m$} |
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510 \end{center} |
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511 \end{itemize} |
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512 |
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513 \only<3->{ |
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514 \begin{textblock}{7}(11,9) |
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515 \begin{tabular}{ll|l} |
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516 \bl{$m =$} & \bl{$16$} & \bl{$16$}\\ |
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517 \bl{$X_0 =$} & \bl{$1$} & \bl{$1$}\\ |
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518 \bl{$a = $} & \bl{$5$} & \bl{$5$}\\ |
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519 \bl{$c =$} & \bl{$1$} & \bl{$0$}\\ |
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520 \end{tabular} |
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521 \end{textblock}} |
492 |
522 |
493 \end{frame}} |
523 \end{frame}} |
494 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
524 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
495 \end{document} |
525 \end{document} |
496 |
526 |