Let U1, U2, ... be a sequence of i.i.d. U (0, 1) random variables. Let N be such that N +1 = min{m e {1,2, ..} : II,U; < e-}. Verify that N follows the Poisson distribution with parameter ). (One may do this by relating to a suitable Poisson process.) Use this result to formulate a method for simulating Poisson(X). [10 marks] %=D1