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$ ./ana_2.pl 16 4 65536
N=65536, V=4, X=65536 integral(65536)=139415.765849051, integral(0)=13
+6533.333333333
...
$ ./ana_2.pl 16 10 32768
N=65536, V=10, X=32768 integral(32768)=191953.190301726, integral(0)=1
+91952.863492063
Expected collisions: 0.326809662627056

$ cat ana_2.pl
#!/usr/bin/perl
...
            +  10*$N   *exp( -1*$X/$N)
            + $X;
}