B.4 - Distribution of $\rho$ implied by uniform priors on $r_1$ and $r_2$

n = 10^7
rM = 100
r1 = runif(n, 0, rM)
r2 = runif(n, 0, rM)
rho = r1/r2
rho.h <- rho[rho<5]       # for the histogram
norma = length(rho.h)/n   # normalization
h <- hist(rho.h, nc=100, plot=FALSE)
h$density <- h$density * norma
h$counts <- h$counts * norma
plot(h, col='cyan', freq=FALSE, main=”, xlim=c(0,5),
     ylim=c(0,0.52),
     xlab=expression(rho), ylab=expression(paste('f(',rho,')')))
abline(v=1, col='red')

# r1.check = rho*r2
# hist(r1.check, nc=200, col='blue', freq=FALSE, xlim=c(0,rM))