using Pkg; Pkg.activate("../."); Pkg.instantiate();
using IJulia; try IJulia.clear_output(); catch _ end

using Plots
using LaTeXStrings

f(y,θ) = θ.^y .* (1 .- θ).^(1 .- y) # p(y|θ)

θ = 0.5
p1 = plot([0,1], f([0,1], θ), 
  line=:stem, marker=:circle, xrange=(-0.5, 1.5), yrange=(0,1), title="Sampling Distribution", xlabel="y", ylabel=L"p(y|θ=%$θ)", label="")

_θ = 0:0.01:1
y=1
p2 = plot(_θ, f(y, _θ), 
  ylabel=L"p(y=%$y | θ)", xlabel=L"θ", title="Likelihood Function", label="")

plot(p1, p2)

using Plots, Distributions, LaTeXStrings

μx = 2.
σx = 1.
μy = 2.
σy = 0.5
μz = μx+μy; σz = sqrt(σx^2 + σy^2)
x = Normal(μx, σx)
y = Normal(μy, σy)
z = Normal(μz, σz)
range_min = minimum([μx-2*σx, μy-2*σy, μz-2*σz])
range_max = maximum([μx+2*σx, μy+2*σy, μz+2*σz])
range_grid = range(range_min, stop=range_max, length=100)
plot(range_grid, pdf.(x,range_grid), label=L"p_x", fill=(0, 0.1))
plot!(range_grid, pdf.(y,range_grid), label=L"p_y", fill=(0, 0.1))
plot!(range_grid, pdf.(z,range_grid), label=L"p_z", fill=(0, 0.1))

open("../../styles/aipstyle.html") do f
    display("text/html", read(f,String))
end