Expected Index of First Occurrence for Binary Patterns of Length 3 in Random Sequences

Date

2025-8-31

Author

Ulusman, Burcu

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This report presents the expected value calculations of the index at which a fixed binary pattern of length three first appears in a random sequence. The theoreti- cal background is based on the graph-theoretic approach proposed by U˘guz (2023), where recurrence relations and generating functions are utilized to compute the relevant probabil- ities. By applying these formulas, explicit expected values are derived for different binary patterns of length three

Subject Keywords

Cryptography, Statistical Randomness Testing, Overlapping Blocks, Generating Functions, Expected Value, Pattern Occurrence in Random Sequences, First Occurrence Index

URI

https://hdl.handle.net/11511/115553

Collections

Graduate School of Applied Mathematics, Thesis