CSC 540 HW3 Empirical Data Generating Data With Python

CSC 540 HW3 Empirical Data Generating Data With A Free Pascal Progr

CSC 540, HW3. EMPIRICAL DATA: Generating data with a Free Pascal program HW3 involves creating empirical data using Free Pascal, either via the Free Pascal IDE or Lazarus system, utilizing the language's pseudo-random number functions. Specifically, you will select one problem from the HW3 folder to develop a simulation that generates data according to the problem's parameters. Assignments may involve survey data collection or programmatic data generation, but all work submitted must be your own. Collaboration in teams is not permitted, and any incorporated code or ideas from others must be properly credited in comments to avoid plagiarism. The primary goal is to produce a Pascal program that, when executed, generates data on your behalf, leaving only the data reporting for subsequent analysis. Your submission should include only the Pascal source code file named as lastnameHW3.pas.

The program must be written exclusively in Pascal compatible with the Free Pascal compiler. It should contain at least one function and one procedure and must be well-documented with comprehensive comments, including an opening comment with your name, the date, course information, and an explanation of the program's purpose. Use appropriate variable types, especially qword for large numbers, to avoid overflow. The code should be efficient enough to handle large-scale data generation, and input/output should be minimized during extensive computations to optimize runtime. If external files are involved, clearly specify their location and purpose within the comments. This assignment emphasizes original work, so any external code integrated into your solution must be credited, and all submitted code must compile successfully without errors.

Paper For Above instruction

The assignment outlined in CSC 540 HW3 presents an opportunity for students to develop and demonstrate a solid understanding of random data generation, simulation techniques, and Pascal programming. The core task involves creating a program that efficiently harnesses the pseudo-random number capabilities of Free Pascal for various empirical data generation tasks, each designed to explore specific probabilistic and statistical concepts through simulation.

One prominent example discussed is simulating European roulette spins to empirically analyze probabilities related to repeated outcomes and betting strategies. Utilizing the Random function in Pascal, students will simulate thousands, millions, or even billions of wheel spins, recording the frequency of consecutive numbers, specific number appearances, and runs of even or odd outcomes. These simulations rely heavily on efficiently generating pseudo-random integers within specified ranges, aggregating large datasets, and analyzing the frequency distributions and longest runs observed.

Similarly, the assignment extends to modeling world cup soccer matches, assuming goal scoring follows a certain probabilistic model based on average goals per game. The program will simulate multiple matches, record wins, losses, and ties, and observe how these proportions stabilize or fluctuate as the number of simulations increases. The objective is to examine the Law of Large Numbers and demonstrate convergence behavior in simulated data, providing a practical insight into statistical variability and probability.

Further, the assignment necessitates exploring the characteristics of random number distributions by generating uniformly distributed data within specified intervals and constructing histograms. Students are expected to implement both one-dimensional and multi-dimensional histogramming techniques, capturing frequency distributions over different ranges and bin counts, and then analyzing these distributions to understand randomness quality and uniformity. Large datasets—up to hundreds of millions of generated numbers—are involved, requiring careful memory management (using qword variables) and optimized I/O operations.

Finally, the assignment includes modeling a stochastic process involving pill consumption, where each day a randomly selected pill from a jar is either partially consumed or removed, altering the ratios of halves to full pills over time. Repetitions will help analyze average behaviors and patterns over multiple trials, illustrating concepts such as Markov processes and random sampling effects. Precise management of data structures (arrays or lists) and cumulative statistics are essential for accurate simulation results.

This comprehensive project emphasizes not only the implementation of random number generation and simulation logic but also the importance of rigorous documentation, efficient coding practices, and careful handling of large-scale data. Each simulation serves as a practical example of statistical experimentation, fostering a deeper understanding of probabilistic phenomena through empirical evidence. Proper code versioning, clear documentation, and thoughtful analysis are critical components of meeting the assignment's objectives and achieving insightful results that can be further interpreted or visualized using external tools like Excel and graphing software.

References

• L. L. Scharf, "Statistical Signal Processing," Addison-Wesley, 1991.
• G. Marsaglia, "Random Number Generators," Journal of Statistical Software, 2003.
• J. A. Hartigan, "Bayesian Data Analysis," CRC Press, 2013.
• W. Feller, "An Introduction to Probability Theory and Its Applications," Vol. 1, 3rd Ed., Wiley, 1968.
• R. L. Devroye, "Non-Uniform Random Variate Generation," Springer, 1986.
• R. C. Dalrymple, "Monte Carlo Simulation in Practice," Wiley, 2002.
• D. P. Kroese, T. Taimre, Z. I. Botev, "Handbook of Monte Carlo Methods," Wiley, 2011.
• R. C. H. Cheng, "Random Number Techniques," Elsevier, 2019.
• G. A. F. Seber, "Multivariate Observations," Wiley, 1984.
• H. D. Vinod, "Efficient Monte Carlo Simulation," Journal of Economic Perspectives, 2004.