@p
1
Btry 694 Class Homework 3
10/2/98
1 Problem 3.4
S ren Hvidkj r
Compare (in a simulation experiment) the performances of the regular Monte Carlo estimator of Z 2 e;x2=2 # = 1 p dx 2 with those of an estimator based on the optimal choice of in

Btry 694 Class Homework 5
11/2/98
1 Problem 5.4
Krishanu Maulik Consider a nite space X and a function H de ned on X .
(a) Show that
8 < 1 expf H (x)g = > M if x 2 O lim X !1 expf H (x)g > 0 otherwise : X where O is the set of global minima of H a

@p
1
Btry 694 Class Homework 6
11/6/98
1 Problem 6.6
Dennis Carlson
Consider a version of A:25] (the independent M-H algorithm), based on a \bound" M on f that is not g f (x) > M for some x. a uniform bound, that is, g(x) f( ) (a) If an accept-re

Btry 694 Class Homework 2
9/17/98
1 Problem 2.1
Dennis Carlson
Referring to example 2.1.4 show that: q (a) The arcsine distribution with density f (x) = 1 x(1 ; x) is invariant under the transform y = 1 ; x, that is, f (x) = f (y). (b) Ths uniform

Homework 1
Class September 7, 1998
1 Problem 1.8
by Mitchell Craig Warachka a) x has Weibull distribution
c xc;1 exp ;xcc
c
(1) (2)
c
cc y c which can be seen as an exponential ( c ) which is a gamma (1 c ).
c using a change of variables x = y 1