Cap. 2

Exercício 2.13

R[t_]=1-(1-Exp[-2t](1-(((1-Exp[-t]))^2)))(1-Exp[-t]);
Simplify[%]

N[(∫_0^(+∞))R[t]\[DifferentialD]t,5]

N[2(∫_0^(+∞))t R[t]\[DifferentialD]t,5]
%-((%%)^2)

Exercício 2.14

R[t_]=(((1-(t/10)))^3);
N[(∫_0^10)R[t]\[DifferentialD]t,5]

N[2(∫_0^10)t R[t]\[DifferentialD]t,5]
%-((%%)^2)

((Sqrt[3.75])/2.5)
N[((Sqrt[(25/3)])/5),5]

Exercício 2.21

λ=1;
Plot[{1-(((1-Exp[-λ t]))^3),Exp[-2λ t](3-2Exp[-λ t]),Exp[-3λ t]},{t,0,5},PlotLegends->Placed[{"limSUP","FF2de3iid","limINF"},Right],
PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]}]

Exercício 2.23

λ=1;
Plot[{1-(((1-Exp[-λ t]))^3),Exp[-2λ t](3-2Exp[-λ t]),Exp[-3λ t]},{t,0,5},PlotLegends->Placed[{"limSUP","FF2de3iid","limINF"},Right],
PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]}]

Plot[{1-(((1-Exp[-λ t]))^3),Exp[-λ t](2-Exp[-λ t]),Exp[-2λ t](3-2Exp[-λ t]),Exp[-2λ t],Exp[-3λ t]},{t,0,5},PlotLegends->Placed[{"limSUP","SUPmmx","FF2de3iid","INFmmx","limINF"},Right],
PlotStyle->{RGBColor[.5,0,0],RGBColor[1,0,0],RGBColor[0,.5,0],RGBColor[0,0,1],RGBColor[0,0,.5]}]