1. 10.Deterministic Randomness 1.Random Sequences

2. 10.1.Random Sequences A sequence of numbers r 1, r 2,... is random if there are no discernible patterns or regularities among them. A set of equally spaced numbers with equal probability of occurrence is called a discrete uniform distribution. A sequence with short range correlation can have an overall randomness : Tests for randomness (Kendall & Smith) : Frequency test : 1 digit. Serial test: 2 digits. Poker test: 5 digits. Gap test: gap between 0s.

3. A random (stochastic) variable is a variable that can take on a set or range of values, each with an associated probability. For a continuous random variable, the probability of finding it with value between r and r + dr is P(r) dr. P(r) = distribution function of the random variable. Uniform distribution P(r) = const. A random number generator generates sequences of uniformly distributed (pseudo-)random numbers.

4. Random Number Generator (Algorithm) Linear Congruence ( Power Residue ) Method To generate sequence { r 1, r 2,..., r k } over interval [ 0, M  1 ] : where a, c are some constants, & r 1 = seed. drand48: Ex.10.1. Do §10.1.2. Ex.10.2. Do §10.1.3.