Question: how to draw it correctly

would like to draw the pdf, however after tried two methods, still can not draw it,

how to draw?

l := [binomial(349,20), binomial(349,8),binomial(349,22),binomial(349,38),binomial(349,49),binomial(349,36),

binomial(349,59),binomial(349,41),binomial(349,32),binomial(349,21),binomial(349,23)];

sl := gfun[listtoseries](l, x, egf);

g := convert(sl, ratpoly);

g := g - subs(x=0, g); 

g := g/subs(x=1.914555911*10^47, g);

dg := diff(g, x);

motion := {diff(f(x), x) - dg*f(x) = 0};

ic := {f(0)=1};

pdf := dsolve(motion union ic);

method 1

with(Statistics):

T := Distribution(PDF=(t->subs(x=t,pdf)));

Ran := RandomVariable(T):

plot(CDF(Ran, x), x = -4 .. 4, legend = "CDF Martin", color = blue);

method 2

A := Sample(Ran, 1, method=[envelope, range=-3..3]):

P := Density(Plot(Ran, range = -3..3, thickness = 3, color=red);

Q := Histogram(A, range = -3..3);

plots[display](P,Q);