Randomness

Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events (or "trials") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.

The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.

Raja

Raja (/ˈrɑːdʒɑː/; also spelled rajah, from Sanskrit राजा rājā-) is a term for a monarch or princely ruler in South and Southeast Asia. Rana is practically equivalent, and the female form Rani (sometimes spelled ranee) applies equally to the wife of a raja or rana. Maharaja, or "great king" is in theory a title for more significant rulers in India, but after some inflation of titles over time, there is no clear difference between the terms.

The title has a long history in the Indian subcontinent and South East Asia, being attested from the Rigveda, where a rājan- is a ruler, see for example the dāśarājñá, the "battle of ten kings".

Etymology

Sanskrit rājan- is cognate to Latin rēx (genitive rēgis), Gaulish rīx, Gaelic rí (genitive ríg), etc., originally denoting heads of petty kingdoms and city states. It is believed to be ultimately derived from the Proto-Indo-European *h₃rēǵs, a vrddhi formation to the root *h₃reǵ- "to straighten, to order, to rule". The Sanskrit n-stem is secondary in the male title, apparently adapted from the female counterpart rājñī which also has an -n- suffix in related languages, compare Old Irish rígain and Latin regina. Cognates of the word Raja in other Indo-European languages include English reign and German reich. Rather common variants in Rajasthani, Marathi and Hindi, used for the same royal rank in parts of India include Rana, Rao, Raol, Rawal and Rawat.