A REVIEW VIDEO ON RANDOM NUMBERS (CHAPTER 5)

A REVIEW VIDEO ON RANDOM NUMBERS (CHAPTER 5). - Roshan Shrestha 23938/076.

Random Numbers. A random number occurs in a specified distribution only when two conditions are met: The values are uniformly distributed over a defined interval or set, and it is impossible to predict future values based on past or present ones..

Properties of Random Number. 1)Uniformity-They are equally probable everywhere. 2)Independence-The current value of random variable has no relation with the previous values..

a) Uniformity Test. Kolmogorov Test. Chi Square Test.

Kolmogorov Test. This test compares the continuous cdf , F(x), of the uniform distribution to the empirical cdf , SN(x), of the sample of N observations. By definition, F(x ) = x, 0 <= x <= 1.

Chi Square Test. .

Independence Testing. a) Gap Test b) Poker Test.

Gap Test. Gap test counts the number of digits that appear between repetitions of particular digit and then uses the Kolmogorov-Smirnov test to compare with the expected size of gaps. The gap test is used to determine the significance of the interval between the recurrences of the same digit. A gap of length x occurs between the recurrences of some specified digit. The following example illustrates the length of gaps associated with the digit 3 : 4, 1, 3, 5, 1, 7, 2, 8, 2, 0, 7, 9, 1, 3, 5, 2, 7, 9, 4, 1, 6, 3 , 3, 9, 6, 3, 4, 8, 2, 3, 1, 9, 4, 4, 6, 8, 4, 1, 3 . There are 7 three’s are there. Thus only six gaps can occur. The first gap is of length 10 and second gap of length 7 and third gap of length zero and so on..

Poker Test. The Poker Test is the test for independence based on the frequency with which certain digits are repeated with in a series of numbers. This test not only tests for the randomness of the sequence of numbers, but also the digits comprising of each of the numbers ..