%test 1c
clearvars


T = 90 + 4*log(31);
%Homogenous process
lambda_h = 1;
t_h = 0;
I = 0;
while 1;
    U = rand(1,1);
    t_h = t_h - (1/lambda_h)*log(U);
    if t_h > T;
        break
    end
    I = I + 1;
    S(I,1) = t_h;
end
for i=1:numel(S);
    S_(i,1) = (1/3)*(-3+4*lambertw(0.75*(exp(3+S(i))).^(1/4)));
end

for n=1:length(S_(:,1));
    S_(n,2) = n;
end

plot(S_(:,1),S_(:,2),'.')