In[]:=
x1=ProbabilityDistribution[2*Sqrt[1-x^2]/Pi,{x,-1,1}]
Out[]=
ProbabilityDistribution,x.,-1,1
2
1-
2
x.
π
In[]:=
Plot[PDF[x1,x],{x,-1,1}]
Out[]=
In[]:=
x2=ProbabilityDistribution[2*Sqrt[1-x^2]/Pi,{x,-1,1}]
Out[]=
ProbabilityDistribution,x.,-1,1
2
1-
2
x.
π
In[]:=
Plot[PDF[x2,x],{x,-1,1}]
Out[]=
In[]:=
X=TransformedDistribution[Abs[x1-x2],{x1ProbabilityDistribution[2*Sqrt[1-x^2]/Pi,{x,-1,1}],x2ProbabilityDistribution[2*Sqrt[1-x^2]/Pi,{x,-1,1}]}]
Out[]=
TransformedDistribution0,ProbabilityDistribution,x.,-1,1ProbabilityDistribution,x.,-1,1,ProbabilityDistribution,x.,-1,1ProbabilityDistribution,x.,-1,1
2
1-
2
x.
π
2
1-
2
x.
π
2
1-
2
x.
π
2
1-
2
x.
π
In[]:=
In[]:=
Y=PDF[X,t]
Out[]=
PDFTransformedDistribution0,ProbabilityDistribution,x.,-1,1ProbabilityDistribution,x.,-1,1,ProbabilityDistribution,x.,-1,1ProbabilityDistribution,x.,-1,1,t
2
1-
2
x.
π
2
1-
2
x.
π
2
1-
2
x.
π
2
1-
2
x.
π
In[]:=
Plot[Y,{t,0,2}]