In[]:=
theta=PDF[TransformedDistribution[ArcCos[2*v-1],vUniformDistribution[{0,1}]],t]
Out[]=
1
2
Abs[Sin[t]]
0<t<π
0
True
In[]:=
r=PDF[TransformedDistribution[v^(1/3),vUniformDistribution[{0,1}]],t]
Out[]=
3
2
t
0<t<1
0
True
In[]:=
phi=PDF[TransformedDistribution[v,vUniformDistribution[{0,2*Pi}]],t]
Out[]=
1
2π
0≤t≤2π
0
True
In[]:=
z=PDF[TransformedDistribution[u*Cos[v],{ur,vtheta}],t]
Out[]=
PDFTransformedDistributionx.1Cosx.2,x.1
3
2
t
0<t<1
0
True
,x.2
1
2
Abs[Sin[t]]
0<t<π
0
True
,t