ma316f03hw10

ma316f03hw10 - MA 316 MATHEMATICAL PROBABILITY...

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

View Full Document Right Arrow Icon
MA 316: MATHEMATICAL PROBABILITY ASSIGNMENT #10 SOLUTIONS: SECTIONS 4.7, 4.8, and 4.4 FALL 2003 4.76: If X 1 and X 2 are independent random variables with normal distributions N (6 , 1) and N (7 , 1) then the distribution of X 1 - X 2 is N (6 - 7 , 1 + 1) = N ( - 1 , 2) so P ( X 1 > X 2 ) = P ( X 1 - X 2 > 0) = P ± ( X 1 - X 2 ) - ( - 1) 2 > 1 2 = 1 - Φ(1 / 2) = 0 . 24 . 4.80: If X 1 and X 2 are independent and X 1 is Poisson with mean μ 1 and Y 1 = X 1 + X 2 is Poisson with mean μ > μ 1 then the moment generating functions of X 1 is M X 1 ( t ) = e μ 1 ( e t - 1) and of Y 1 is M Y 1 ( t ) = e μ ( e t - 1) . Since X 2 = Y 1 - X 1 then the moment generating function of X 2 is M X 2 ( t ) = E [ e t ( Y 1 - X 1 ) ] = E [ e tY 1 e t ( - X 1 ) ] = E [ e tY 1 ] E [ e t ( - X 1 ) ] = e μ 1 ( e t - 1) e - μ 1 ( e t - 1) = e ( μ - μ 1 )( e t - 1) which shows that X 2 is Poisson with parameter μ - μ 1 . 4.81:
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/10/2009 for the course STATS 517 taught by Professor Song during the Fall '07 term at Purdue.

Page1 / 2

ma316f03hw10 - MA 316 MATHEMATICAL PROBABILITY...

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