If you want to obtain a density distribution proportional to 1/sqrt(x) for x in some finite interval [a,b], you can proceed as follows. The cumulative probability function must be:
cdf(x) = (sqrt(x)-sqrt(a))/(sqrt(b)-sqrt(a))
which you get by integrating 1/sqrt(x) from a to x and adjusting the proportionality constant to get a cdf(b)=1 for the entire interval from a to b.
To generate this using rand, set the above cdf(x) to r = rand and solve for x:
r = rand;
x = (sqrt(a)+(sqrt(b)-sqrt(a))*r).^2;
This illustrates how one would proceed to use rand for generating any given probability density function. It depends on being able to solve for x in an equation cdf(x) = r.