> with(Statistics);
> with(plots);
> 
> X := RandomVariable(Normal(0, 1));
> t := Quantile(X, .375);
> S := Sample(X, 100);
> S[1];
> op(1, S);
> 
> 
> Intconf := proc (Sam, s, alpha) n := op(1, Sam); t := Quantile(RandomVariable(Normal(0, 1)), 1-(1/2)*alpha); m := Mean(Sam); [m-s*t/sqrt(n), m+(s.t)/sqrt(n)] end proc;
> Intconf(S, 1, 0.5e-1);
> Intconf2 := proc (Sam, alpha) n := op(1, Sam); t := Quantile(RandomVariable(StudentT(n-1)), 1-(1/2)*alpha); m := Mean(Sam); s := StandardDeviation(Sam); [m-s*t/sqrt(n), m+(s.t)/sqrt(n)] end proc;
> Intconf2(S, 0.5e-1);
> 
> S2 := Sample(RandomVariable(Normal(2.5, 3)), 50);
> Imin := [seq(evalf(Intconf(S2, 3, (1/100)*i)[1]), i = 1 .. 100)];
> Imax := [seq(evalf(Intconf(S2, 3, (1/100)*i)[2]), i = 1 .. 100)];
> P1 := plot([seq([(1/100)*i, Imin[i]], i = 1 .. 100)]);
> P2 := plot([seq([(1/100)*i, Imax[i]], i = 1 .. 100)]);
> display(P1, P2);
> Interv := [seq(evalf(Intconf(S, 3, (1/100)*i)), i = 1 .. 100)];
> plot([seq([(1/100)*i, Interv[i][1]], i = 1 .. 100)]);
> 
> Imin2 := Array(1 .. 200); Imax2 := Array(1 .. 200);
> N := 0; for i to 200 do S := Sample(RandomVariable(Normal(2.5, 3)), 300); Imin3[i] := Intconf(S, 3, .1)[1]; Imax3[i] := Intconf(S, 3, .1)[2]; if `and`(evalf(Imin3[i]) < 2.5, evalf(Imax3[i]) > 2.5) then N := N+1 end if end do; (1/200)*N;
> U := Sample(RandomVariable(Uniform(0, 1)), 500);
> Xu := map(proc (t) options operator, arrow; 4*sqrt(1-t^2) end proc, U);
> Mean(Xu);
> StandardDeviation(Xu);
> 
> evalf(Intconf2(Xu, 0.5e-1));
> V := Sample(RandomVariable(Uniform(0, 1)), 10000); Xv := map(proc (t) options operator, arrow; 4*sqrt(1-t^2) end proc, V);
> W := CumulativeSum(Xv);
> plot([seq([i, abs(W[i]/i-Pi)], i = 1 .. 10000)]);
> for i to 500 do if V[2*i]^2+V[2*i+1]^2 < 1 then Y[i] := 4 else Y[i] := 0 end if end do;
> StandardDeviation(convert(Y, list));
> evalf(Intconf2(convert(convert(Y, list), Vector), 0.5e-1));
> 
> evalf(Intconf2(Xv, 0.5e-1));
>