lambda := .2;
                              0.2
mu := .3;
                              0.3
F := proc (n)

exp(-lambda*t)*(lambda*t)^n/factorial(n)

end proc;
P := proc (n) local ret, i; ret := 0;

for i from 0 to n do

if i = 0 then ret := ret+evalf(exp(-lambda*t))

elif i = 1 then ret := ret+evalf((diff(exp(-lambda*t), t))/mu+lambda*exp(-lambda*t)/mu)

elif i < n then ret := ret+evalf((diff(exp(-lambda*t)*(lambda*t)^(n-1)/factorial(n-1), t))/mu+(lambda+mu)*exp(-lambda*t)*(lambda*t)^(n-1)/(mu*factorial(n-1))-lambda*exp(-lambda*t)*(lambda*t)^(n-2)/(mu*factorial(n-2)))

else ret := ret-(diff(exp(-lambda*t)*(lambda*t)^n/factorial(n), t))/mu+lambda*exp(-lambda*t)*(lambda*t)^(n-1)/(mu*factorial(n-1)) end if

end do;

ret

end proc;