sol9 - STA3007 Applied probability(08-09 Solution to...

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: STA3007 Applied probability (08-09) Solution to Assignment 9 Chapter 5 Problem 6.2 The key observation is that, if θ is uniform on [0 , 2 π ), and Y is independent of θ and has an arbitrary distribution, then Y + θ (mod 2 π ) is uniform on [0 , 2 π ). The proof of this statement may be difficult, but it is clear by intuition. As the particles are distributed on the surface of a circular region according to a spatial Poisson process, the angle of the polar coordinates of each point is uniformly distributed on [0 , 2 π ). Therefore, at the end of the point movement process, the points are still Pois- son distributed over the region. Problem 6.3 Without loss of generality, let a be a nonnegative integer. Let T be the time of system failure, then { T > t } if and only if { Z ( t ) < a } . By observing Pr( T > t ) = Pr( Z ( t ) < a ) = Pr( Z ( t ) < = a- 1) , we have E( T ) = 1 λ ∞ X n =0 G ( n ) ( a- 1) = 1 λ " 1 + ∞ X n =1 G ( n ) ( a- 1) # = 1 λ " 1 + ∞ X n =1 a- 1 X k =0...
View Full Document

This note was uploaded on 02/16/2011 for the course ECON 1224 taught by Professor Afdsa during the Spring '11 term at CUHK.

Page1 / 4

sol9 - STA3007 Applied probability(08-09 Solution to...

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