# Random Sampling By A Given Probability Distribution

### Problem Definition:

Random select a number i (i >= 1 and i < = n), from 1 to n where n >= 1 given a probability discrete distribution P: Pr(1) = p1, Pr(2) = p2, …, Pr(n) = pn, such that p1 + p2 + … pn = 1, that is, the probability i would be selected should be equal to Pr(i).

### Source code:

The whole process is quite like a spin process, imagine a wheel of area 1 which is separated into n sector and the, Sector i is of area Pr(i). There is a needle at the 12 clock, and then we spin the wheel, we choose the sector k where the needle stays at in the when the wheel stops. The following is the matlab source code with a simplified implementation:

function sel = spin(prob) % @Desc this function takes a probability distribution % and a candidate i will be returned with probability prob(i) % @Param sum(prob) should be 1 % prob is n * 1 column vector % if sum(prob) - 1 > eps error('Error occurred in spin(prob): sum(prob) != 1\n'); end rnd_value = rand(); % between 0 and 1 n = size(prob, 1); sel = 0; % undefined! cum = 0.0; for i = 1:n cum = cum + prob(i); if cum >= rnd_value sel = i; break; end en

To summarize, I give a matlab implementation for how to randomly select a number out of a set of numbers with given probability.