Probability and statistics
Probability and statistics, also called statistics and probability, are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics.
Forms of probability and statistics were developed by Arab mathematicians studying cryptology between the 8th and 13th centuries. Al-Khalil (717–786) wrote the Book of Cryptographic Messages which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels. Al-Kindi (801–873) made the earliest known use of statistical inference in his work on cryptanalysis and frequency analysis. An important contribution of Ibn Adlan (1187–1268) was on sample size for use of frequency analysis.