Conditional Distributions
The goal is to provide a general denition of the conditional distribution of Y given X ,
when (X, Y ) are jointly distributed.
Let F be a distribution function on R. Let G(, ) be a map from R BR to [0, 1]
satisfying: (a) G(x, ) i
Stat 610Assignment 1
Graded Questions
(1) Chapter 1, Problem 4.
(2) Chapter 1, Problem 9.
(3) Chapter 1, Problem 14.
(4) Chapter 1, Problem 30, parts ad.
Additional Questions
Chapter 1, Problems 1, 8, 10, 16, 18, 19, and 26.
Evaluate the following limit
Stat 610Assignment 2
Graded Questions
(1) Chapter 1, Problem 29.
(2) Chapter 1, Problem 30, part e.
(3) Chapter 1, Problem 34.
Additional Questions
Chapter 1, Problems 23, 25, 26, 27, 28, and 33.
CHAPTER 4
Integration
In this Chapter, we dene the integral of real-valued functions on an arbitrary
measure space and derive some of its basic properties. We refer to this integral as
the Lebesgue integral, whether or not the domain of the functions is s
Statistics 610: Homework 1
Moulinath Banerjee
University of Michigan
Sept 20, 2013
Announcement: The homework carries 90 points and is due on 4th Oct, Friday
1. Consider R equipped with the -eld of countable/co-countable sets. Thus, a set A belongs
to the
Simple Random Sampling
Moulinath Banerjee
University of Michigan
September 2, 2013
1
Simple Random Sampling
The goal is to estimate the mean and the variance of a variable of interest in a nite
population by collecting a random sample from it. Suppose the
Principles of Parametric Inference
Moulinath Banerjee
University of Michigan
September 2, 2013
The object of statistical inference is to glean information about an underlying population
based on a sample collected from it. The actual population is assumed
Measure Theory Pre-requisites
Moulinath Banerjee
University of Michigan
September 10, 2013
1
Measure Spaces
We start with a measure space (, A, ). The set is the sample space and a generic point
in this set is denoted . The entity A is a collection of sub
Information Inequality
We start with the Hammersley-Chapman-Robbins inequality as in Keener (2010). Suppose
(X ) is an unbiased estimator of g () in a parametric model (here X could be a vector or scalar)
and is an arbitrary random variable. Then, we hav
PRACTICE FINAL EXAMStatistics 610
(1) Consider a multinomial experiment in which there are n trials
and three categories. The categories have probabilities , and
12, where is an unknown parameter in (0, 1/2). The counts
for these categories are X1 , X2 an