rcd example is slow

[zenna]

The following code from Omega Models is slow for two reasons that need to be fixed.

1. We are using samplemean instead of the symbolic mean but in this case we should be able to use symbolic mean
2. Even using samplemean it takes a much longer time on my machine (around minutes) than I would expect. Maybe my expectations are wrong or maybe something weird is happening. Need to profile.

using Omega 
using Plots

faircoin = bernoulli(0.5, Bool)
headsbiased = bernoulli(0.5, Bool)
function weight_(ω)
  weight = if faircoin(ω)
    0.5
  elseif headsbiased(ω)
    0.6
  else
    0.4
  end
end
weight = ciid(weight_)
coin = bernoulli(weight, Bool)
coinrcd = coin ∥ (faircoin, headsbiased)

# Compute the expectation using nsamples
meannsamples = 100000
probdist = Omega.samplemeanᵣ(coinrcd, meannsamples)

# Draw nsamples from the conditional expectation
nsamples = 100
probsamples = [rand(probdist) for i = 1:nsamples]

fig = histogram(probsamples, nbins=100, xlims=[0.0, 1.0], normalize=true, size=(400, 300), label="")
savefig(fig, "coindist.png")