Stat 5132 (Geyer) Old Second Midterm Solutions

Stat 5132 (Geyer) Old Second Midterm Solutions - Up: Stat...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Up: Stat 5132 Midterm 2 Problem 1 (a) This is a special case of homework problem 8-4 in the notes. The problem statement says that where . (Here and s are fixed numbers calculated from the data, and denotes a random variable with the posterior distribution of given the data.) The distribution of T is symmetric about zero, so E ( T ) = 0 when the expectation exists (which the problem says to assume). Thus by linearity of expectation . (b) Same as part (a). When a distribution has a center of symmetry, then the center of symmetry is the the median as well the mean when the mean exists. Thus is also the posterior median. Problem 2 (a) The likelihood is The prior is omitting constants that are functions of and but not (normalizing constants of the prior cancel out in calculating the posterior). Thus the unnormalized posterior is
Background image of page 1

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

View Full DocumentRight Arrow Icon
This is an unnormalized density. Thus that is the posterior distribution of given X . (b)
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/28/2010 for the course STAT 5101 taught by Professor Staff during the Spring '02 term at Minnesota.

Page1 / 5

Stat 5132 (Geyer) Old Second Midterm Solutions - Up: Stat...

This preview shows document pages 1 - 3. Sign up to view the full document.

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