Hidden correlation

mixture.jl

using GLMakie
using Random 

# mixture distribution
X(c) = rand() < c ? sqrt(rand()) :  1 - sqrt(rand())

# sample
Random.seed!(1);
A = [0:0.01:1;; X.(0:0.01:1)]; 

# correlation
cor(A)
# 2×2 Matrix{Float64}:
#  1.0       0.284633
#  0.284633  1.0

# plot
fig = Figure()
ax = Axis(fig[1,1])
scatter!(ax, A)
ax = Axis(fig[1,2])
image!(ax, [x*y + (1-x)*(1-y) for x in 0:0.1:1, y in 0:0.01:1], colormap=:viridis )
save("density.png", fig)