De acuerdo. No lo sabía. Lo he exportado desde el Mathematica como .gif, llamando gif = Manipulate[ etc...], y luego Export["hello.gif",gif]. No sé si habrá más opciones en el Mathematica para .gif. Saludos.
p1 = {1/3, 0};
p2 = {2/3, 0};
f[x_] := p^(3 x) (1 - p)^(3 (1 - x)); (* Maximum of f is for p = x *)
g[x_, p_] := p^(3 x) (1 - p)^(3 (1 - x)); (* Auxiliary function for plotting the max *)
Manipulate[
Show[
Plot[f[x], {p, 0, 1},
PlotStyle -> {Blue, Thickness[0.008]},
PlotPoints -> 100,
PlotRange -> {{-0.05, 1.025}, {-0.05, 1.025}},
Ticks -> {Range[0, 1, .1], Range[0, 1, .1]},
AspectRatio -> Automatic],
Graphics[{Thickness[0.005], Line[{p1, {1/3, 1}}]}],
Graphics[{Thickness[0.005], Line[{p2, {2/3, 1}}]}],
Graphics[{Pink, PointSize[0.05/2], Point[{p1, p2}]}],
Graphics[{Green, PointSize[0.05/2], Point[{x, g[x, x]}]}],
Graphics[{Thickness[0.005/2], Line[{{x, 0}, {x, g[x, x]}}]}],
Graphics[{Thickness[0.005/2], Line[{{0, g[x, x]}, {x, g[x, x]}}]}]
]
, {{x, 0.001, "x"}, 0 + 0.001, 1 - 0.001, .01}]