distribucions de probabilitat

f(k) = [ n // k ]·2^{(-n)}


f(0)+...+f(n) = ( [ n // 0 ]+...+[ n // n ] )·2^{(-n)}=2^{n}·2^{(-n)}=1


f(k) = [ n // k ]·p^{(n+(-k))}·(1+(-p))^{k}


f(0)+...+f(n) = ( [ n // 0 ]p^{n}+...+[ n // n ](1+(-p))^{n} )=( p+(1+(-p)) )^{n}=1


f(k) = (1/p^{n})·( p^{k}+(-1)·p^{(k+(-1))} )


f(0)+...+f(n) = ( (1/p^{n})·( ( (p^{n+1}+(-1))/(p+(-1)) )+(-1)·( (p^{n}+(-1))/(p+(-1)) ) )=...
...(1/p^{n})·p^{n}·( (p+(-1))/(p+(-1)) )=1