Random Number Generators. x n = f ( x n-1 , x n-2 ) where x 0 is seed Pseudo-random since, given the same seed, the sequence is repeatable and deterministic Cycle length – length of repeating sequence Example: x n = a x n-1 + b mod m. seed. cycle. period. k. D = S.
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xn = f ( xn-1, xn-2) where x0 is seed
D = S
(oi – ei)2
i=1Testing Random Numbers
Sum = 10.38 whereas X 2[0.9;9] = 14.68
K+ = n max [Fo(x) – Fe(x)]
K- = n max [Fe(x) – Fo(x)]
xTesting Random Numbers
Fo(xi) – Fe(xi)
Fe(xi+1) – Fo(xi)
j/n - xj
xj – (j-1)/n
Rk = S
(Ui – ½)(Ui+k – ½)
Rk! z1-a/2 /(12 n-k)Testing Random Numbers
What does a test say about this sample?
-> discussion of timing-firstpaper