Lecture 3 Pseudo-random number generation
Lecture 3 Pseudo-random number generation
Lecture 3 Pseudo-random number generation
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Idea 1: Discrete distributions<br />
Coin toss distribution: P(X = 1) = 0.5, P(X = 0) = 0.5<br />
(1) Generate U ∼ U(0, 1)<br />
(2) If U ≤ 0.5 then Z = 1, otherwise Z = 0<br />
Z has a coin toss distribution.<br />
Discrete distribution: P(X = ai) = pi, i = 1, 2,... ,n<br />
(1) Compute ck = � k<br />
i=1 pi<br />
(2) Generate U ∼ U(0, 1)<br />
(3) Find smallest k such that U ≤ ck. Put Z = ak<br />
Z has a given discrete distribution.<br />
Computational Finance – p. 20