Let equal the sum of n rolls of an m -sided die. Use animation to graph probability histograms of the p.d.f. of .

First an example of how the Convolution program works using the sum of two m -sided dice.

> m := 4:
k := 'k':

> domain := [k\$k=1..m];
probs := [1/m\$k=1..m];
X[1] := zip((x,y)->(x,y),domain,probs);
P1 := ProbHistFill(X[1]):
P2 := plot([[0,0],[0,0]], x = 0 .. 4.7, xtickmarks=domain, labels=[``,``], title = `Probability Histogram, One 4-sided Die`, titlefont=[TIMES,BOLD,14]):
display({P1, P2});

> Y[2] := Convolution(X[1], X[1]);

> k := 'k':
xtics := [k\$k=1..8]:
P2 := ProbHistFill(Y[2]):
T := plot([[0,0],[0,0]], x = 0 .. 8.7, xtickmarks=xtics, labels=[``,``], title = `Probability Histogram,\nSum of Two 4-sided Dice`, titlefont=[TIMES,BOLD,14]):
display({P2, T});

Now use animation on n to show the probability histograms for the p.d.f. of the sum of n m -sided dice.

2. Let equal the sum of n rolls of an m -sided die. Use animation to graph probability histograms of the p.d.f. of . Superimpose a normal p.d.f. with mean and variance .

Probability Histogram, Sum of n m -sided Dice, N ( , ) p.d.f.