# Sum of random jumps in the plane
function rsum(n::Int)
    p = 1.0
    for j in 2:n
        p += exp(2pi * im * rand())
    end
    return p
end

# Distance after n random jumps
function rd(n::Int)
    abs(rsum(n))
end

 # Data array to build an histogram
 function sim(n::Int, m::Int = 22)
    datos = zeros(2^m) # Creamos la matriz de datos a rellenar
    for i in 1:2^m
        datos[i] = rd(n)
    end
    return datos
 end

# Plotting densities
using StatsPlots, Statistics
function dd(n::Int,m::Int=22)
    x = sim(n,m)
    density!(x, w = 2,
        xlabel = "Distance", #"Distancia recorrida",
        label = "Estimated density for $n jumps",
        fill = (0, 0.1, :orange))
    vline!([mean(x)],
        label = "Estimated mean for $n jumps: $(round(mean(x),digits=2))",
        line = :dash)
end