Sol_hw_3 - ASSIGNMENT 3 - SOLUTIONS 1. Exercise 1 The rst...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ASSIGNMENT 3 - SOLUTIONS 1. Exercise 1 The rst algorithm of simulation is the inverse method, applied to this distribution. The pseudo-code is the following: (1) := k j =0 e- j j ! (2) p := - 1 e- i := 0 F := p (3) U := Uniform (0 , 1) (4) while ( U > F ) i := i + 1 p := p i F := F + p (5) Return F The second method to generate the random variable is applying the acceptance/rejection method. We will use a discrete uniformly distributed random variable over the set { ,...,k } as auxiliary distribution. Let = k j =0 e- j /j ! . Since we know that the mode of the Poisson distribution is d e , we have that e- j /j ! e- d e / d e ! j . Our bound for this case will be C = - 1 e- d e / d e ! . De ne the desired distribution probability mass function as p ( i ) = P { X = i } and q ( i ) = 1 / ( k + 1) i = 0 ...k (note that our bound can be written as C = p ( d e ) ). The method is then de ned as follows: (1) :=...
View Full Document

Page1 / 3

Sol_hw_3 - ASSIGNMENT 3 - SOLUTIONS 1. Exercise 1 The rst...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online