Let U1, U2, ... be a sequence of i.i.d. U(0, 1) random variables. Let N be...

 

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