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X = c(1,0,0)

plot(function(p) likelihood_bin_mix(x = X, pi = p), xlim = c(.33,.34)); abline(v = 4*mean(X) - 1)

plot(function(p) likelihood_bin_mix(x = X, pi = p), xlim = c(0,1)); abline(v = 4*mean(X) - 1)

plot(function(p) likelihood_bin_mix(x = X, pi = p) |> log(), xlim = c(0,1)); abline(v = 4*mean(X) - 1)