Lecturenotes16 - STAT 430/510 Lecture 16 STAT 430/510...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 430/510 Lecture 16 STAT 430/510 Probability Hui Nie Lecture 16 June 24th, 2009
Image of page 1

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

View Full Document Right Arrow Icon
STAT 430/510 Lecture 16 Review Sum of Independent Normal Random Variables Sum of Independent Poisson Random Variables Sum of Independent Binomial Random Variables Conditional Distributions: Discrete Case
Image of page 2
STAT 430/510 Lecture 16 Conditional Distributions: Continuous Case Let X and Y be jointly continuous r.v.’s. Then for any x value for which f X ( x ) > 0, the conditional pdf of Y given X = x is f Y | X ( y | x ) = f ( x , y ) f X ( x ) , - ∞ < y < For any set A , P ( Y A | X = x ) = Z A f Y | X ( y | x ) dy = Z A f ( x , y ) f X ( x ) dy If X and Y are independent, then f Y | X ( y | x ) = f ( x , y ) f X ( x ) = f X ( x ) f Y ( y ) f X ( x ) = f Y ( y )
Image of page 3

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

View Full Document Right Arrow Icon
STAT 430/510 Lecture 16 Example The joint density of X and Y is given by f ( x , y ) = 12 5 x ( 2 - x - y ) , 0 < x < 1 , 0 < y < 1 0 , otherwise Compute the conditional density of X given that Y = y , where 0 < y < 1. f X | Y ( x | y ) = f ( x , y ) f Y ( y ) = x ( 2 - x - y ) R 1 0 x ( 2 - x - y ) dx = 6 x ( 2 - x - y ) 4 - 3 y
Image of page 4
STAT 430/510 Lecture 16 One Discrete R.V. and one Continuous R.V.
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern