rvs=Table[{RandomReal[],RandomReal[]},{10000}];

ListPlot[rvs,AxesOrigin->{0,0}]

(* our center is 0.5,0.4  ,radius =0.3*)

inCircle[pt_]:=If[   (Sqrt[(((pt[[1]]-0.5))^2)+(((pt[[2]]-0.4))^2)])≤ 0.3,   True,  False]

inCircleRvs=Select[rvs,inCircle];

ListPlot[inCircleRvs,AxesOrigin->{0,0}]

((Length[inCircleRvs])/10000.)

area=π (0.3^2)

Random Phase

zAngles=Table[RandomReal[{-π,π}],{(10^5)}];

realizations=Map[Cos[2 π t + #]&,zAngles];

Plot[realizations,{t,-0.7,1.2}]

valAt1 = realizations /.t->1;

Histogram[valAt1]

Plot[(1/(π(Sqrt[1-(y^2)]))),{y,-1,1}]

Integrate[(1/(π(Sqrt[1-(y^2)]))),{y,-0.9,-0.3}]

Length[Select[valAt1,(#>-0.9 && # <-0.3 )&]]