Practice Exam (with solutions)
Please note. These are sample questions. They should not be taken to indicate the precise coverage or
diculty of the actual exam.
1. Suppose that X1 , X2 , . . . , Xn are a sample from the density
2 x
0
f (x; ) =
2 1
0<x<1
Mathematical Statistics Midterm Exam Answers
This is just for practice!
March 2, 2013
Please solve all 4 problems and all parts of each problem.
Each problem counts the same amount (24 points).
Identify your answers by drawing boxes around them.
Only
2
r.- ; tics 3 445
A p r i l5 . 2 0 1 2
Name:
e
This i s a c losed ook xarniDation, xceptt hat y ou m tly u seo ne t heet o f y our o wn n otesa Dd a
b
o
D isplayy our l easonirlg n t he i nsidep agesw ith a s n ruchd etail a nd a s c learly a )l
calculat
Exam 1
Statistics 3445
February 23, 2012
Name:
This is a closed book examination, except that you may use one sheet of your own notes
and a calculator. Display your reasoning on the inside pages with as much detail and as
clearly as possible (unsupported
Exam 3
Statistics 3445
May 3, 2012
Name:
This is a closed book examination, except that you may use one sheet of your own notes and a
calculator. Display your reasoning on the inside pages with as much detail and as clearly as
possible (unsupported an
Cramer-Rao Bound
Konstantinos G. Derpanis
September 8, 2006
The Cramer-Rao bound establishes the lower limit on how much information about an unknown
probability distribution parameter a set of measurements carries. More specically, the inequality
establi
6.5
Conditional Distributions
General Bivariate Normal
Let Z1 , Z2 N (0, 1), which we will use to build a general bivariate normal
distribution.
Lecture 22: Bivariate Normal Distribution
f (z1 , z2 ) =
Statistics 104
12
1
2
exp (z1 + z2 )
2
2
We want to t
Outline Chapter 10
1. General Binary Trees 2. Binary Search Trees 3. Building a Binary Search Tree 4. Height Balance: AVL Trees 5. Splay Trees: A Self-Adjusting Data Structure
Binary Trees
Binary Trees
Binary Trees (cont)
The Binary trees with three nodes
Outline
Chapter 9
TABLES AND
INFORMATION RETRIEVAL
Introduction: Breaking the lg n Barrier
By use of key comparisons alone, it is impossible to
complete a search of n items in fewer than lg n comparisons,
on average (lowerbound_search_thm ).
Ordinary tabl
Outline
1. Introduction to Recursion
Chapter5
2. Principles of Recursion 3. Backtracking: Postponing the Work 4. Tree-Structured Programs: Look-Ahead in Games
RECURSION
Stacks and Trees
Stacks and Trees (cont)
THEOREM During the traversal of any tree, ver
Outline
Chapter 2
INTRODUCTION TO
STACKS
1. Stack Specifications
2. Implementation of Stacks
3. Application: A Desk Calculator
4. Application: Bracket Matching
5. Abstract Data Types and Their Implementations
Stacks
A stack is a data structure in which al