(* See 15.6.2 of Numerical Recipes *)

(* Make some mock data // 100 points to simplify calculations *)
SeedRandom[12345];
data=RandomReal[{0,1},{100}];

(* Make 10000 realizations based on the data and measure which ones are replaced *)
dd=Table[RandomChoice[data,100]//Sort//Union//Length,{10000}];

(* Compare exact result (~1/e) with numerical one and make histogram *)
Print["% of points not replaced (exact)    = ",1-1/E//N]
Print["% of points not replaced (numerical)= ",dd/100//Mean//N]

SmoothHistogram[dd,1, Filling->Axis,Frame->True,Epilog->{Red,Dashed,Line[100{{1-1/E,0},{1-1/E,1}}]},Axes->False,FrameStyle->Black,FrameLabel->{"%","PDF"},BaseStyle->FontSize->14]