RandomInteger[{20,100}]
RandomReal[{20,100},{10,3}]
RandomChoice[{a,b,c},20]
RandomVariate[NormalDistribution[],10]

Plot[
Evaluate[
Table[
PDF[NormalDistribution[0,σ],x]
,{σ,{.75,1,2}}
]
],{x,-6,6},Filling->Axis]

Plot[
Evaluate[
Table[
CDF[NormalDistribution[0,σ],x],
{σ,{.75,1,2}}
]
],{x,-6,6},Filling->Axis]

data1=RandomVariate[NormalDistribution[0,0.5],2500];
data2=RandomVariate[TriangularDistribution[{-1,1}],2500];
ListPlot[{data1,data2}]

data=RandomVariate[NormalDistribution[],2500];
Mean[data]
Variance[data]
{{Histogram[data],Histogram[data,Automatic,"PDF"]},
{SmoothHistogram[data],SmoothHistogram[data,Automatic,"PDF"]}}//TableForm

{{SmoothHistogram[data,Automatic,"PDF",PlotLabel->"Плотность вероятности"],SmoothHistogram[data,Automatic,"CDF",PlotLabel->"Функция распределения"]},{SmoothHistogram[data,Automatic,"SF",PlotLabel->"Функции надёжности"],
SmoothHistogram[data,Automatic,"HF",PlotLabel->"Интенсивность отказов"],SmoothHistogram[data,Automatic,"CHF",PlotLabel->"Распределение интенсивность отказов"]}}//TableForm

(*data=RandomVariate[NormalDistribution[],2500];*)
(*data=RandomVariate[TriangularDistribution[{-1,1}],2500];*)
data=RandomVariate[NormalDistribution[0,1],2500];
test=DistributionFitTest[data,Automatic,"HypothesisTestData"];
test["TestDataTable",All]

FindDistribution[data]

Show[
Histogram[data,Automatic,"ProbabilityDensity"],
Plot[PDF[NormalDistribution[],x],{x,-5,5},PlotStyle->Red],
Plot[PDF[test["FittedDistribution"],x],{x,-5,5},PlotStyle->Green]
]

test["Properties"]

ProbabilityPlot[data,NormalDistribution[0,1]]

data1=RandomVariate[NormalDistribution[],100];
data2=RandomVariate[NormalDistribution[1,1],1000];
SmoothHistogram[{data1,data2},Automatic,"CDF"];

ProbabilityPlot[{data1,data2},StudentTDistribution[1]]

{{DistributionChart[data2],BoxWhiskerChart[data2]}}//TableForm

PairedHistogram[data1,data2]
PairedHistogram[data1,data2,Automatic,"PDF"]

Histogram3D[RandomVariate[NormalDistribution[0,1],{500,2}]]

data1=RandomVariate[NormalDistribution[0,1],{500,2}];
data2=RandomVariate[NormalDistribution[3,1/2],{500,2}];
Histogram3D[{data1,data2}]
SmoothHistogram3D[{data1,data2},PlotRange->Full]

inset=ListPlot[data2,PlotRange->{{0,5},{0,5}},AspectRatio->1,Frame->True,ImageSize->150,PlotStyle->Black,PlotLabel->Text[Style["Old Faithful Geyser Data","Label"]],Background->Directive[Opacity[.5],White],Axes->None];

SmoothHistogram3D[data2,PlotRange->All,Mesh->25,PlotLabel->Text[Style["Duration vs. Waiting\[Hyphen]Time","Label",Large]],PlotPoints->100,ColorFunction->"BrownCyanTones",MeshStyle->Directive[Opacity[.3]],MeshFunctions->{#2&,#1&},ViewPoint->{2,-2,1},Epilog->Inset[inset,{Right,Bottom},{Right,Bottom}],ImageSize->600,BaseStyle->{FontFamily->"Helvetica"},LabelStyle->Bold]

DensityHistogram[data1,{0.2},ColorFunction->"DarkRainbow",Method->{"DistributionAxes"->"Histogram"},ChartBaseStyle->Directive[FaceForm[Opacity[1]],EdgeForm[White]],ImageSize->500,BaseStyle->{FontFamily->"Helvetica"},LabelStyle->Bold]

back=ImageData[Rasterize[SmoothHistogram[data2[[All,1]],Axes->None,PlotRange->{{0,7},All},PlotStyle->Red,Filling->{1->{Axis,Red}},PlotRangePadding->Scaled[0.02]],Background->None]];

left=ImageData[Rasterize[SmoothHistogram[data2[[All,2]],Axes->None,PlotRange->{{0,7},All},Filling->{1->{Axis,Blue}},PlotRangePadding->Scaled[0.02]],Background->None]];

Show[
SmoothHistogram3D[data2,PlotRange->All,Mesh->25,PlotPoints->100,ColorFunction->"BrownCyanTones",MeshStyle->Directive[Opacity[.3]],
Epilog->Inset[inset,{Right,Bottom},{Right,Bottom}],ImageSize->600,BaseStyle->{FontFamily->"Helvetica"},LabelStyle->Bold]
,
Graphics3D[{{Texture[back],Polygon[{Scaled[{0,1,0}],Scaled[{1,1,0}],Scaled[{1,1,1}],Scaled[{0,1,1}]},VertexTextureCoordinates->{{0,0},{1,0},{1,1},{0,1}}]},{Texture[left],Polygon[{Scaled[{0,0,0}],Scaled[{0,1,0}],Scaled[{0,1,1}],Scaled[{0,0,1}]},VertexTextureCoordinates->{{0,0},{1,0},{1,1},{0,1}}]}}]
]

Probability[-0.1<=x≤0.1,x\[Distributed]NormalDistribution[]]//N

a=CDF[NormalDistribution[],-0.1]
b=CDF[NormalDistribution[],0.1]
b-a