ST1131 Introduction to Statistics
DSAP
Solution
Tutorial 5
Lecture 9 & 10: Probability Distributions
1.
(6.2) Move first in Monopoly:
In Monopoly, dice are first used to determine which player gets to move first. Suppose
there are two players in the game.
ST1131 Introduction to Statistics
DSAP
Solution
Tutorial 2
Lecture 3 & 4 : Numerically Summarizing Data
1.
(2.40) Net worth by degree:
a. Some people who make a huge amount of money inflate the mean; these inflated
values (outliers) do not affect the medi
Lets revise
l is an eigenvalue of A det(lI A) = 0
0 is an eigenvalue of A det( A ) = 0
A is invertible 0 is not an eigenvalue of A.
The eigenvalues of a triangular matrix are the
diagonal entries.
The eigenvectors of A are the non-trivial
non trivial
Lets revise
Let A be an n n matrix
A is diagonalizable if and only if A has
n linearly independent eigenvectors
A set of eigenvectors associated with different
eigenvalues are linearly independent
If the sum of the dimensions of all eigenspaces
g
of
A
Lets revise
A linear transformation T : Rn Rm
is a mapping between two vector spaces
is defined by matrix multiplication
maps zero vector to zero vector
preserves linear combinations
If T(u) Au for all u Rn, then A is the
standard matrix of T
If cfw
Lecture 16
6.1 Eigenvalues
g
and Eigenvectors
g
6.2 Diagonalization
Chapter 6
Diagonalization
1
Section 6.1
61
Eigenvalues and Eigenvectors
Objectives
What are Eigenvalues, Eigenvectors and
Eigenspace?
How to find eigenvalues and eigenvectors of a
matri
Lets revise
uv = uvT
(RHS is matrix multn, u, v as rows)
uv = uTv
(RHS is matrix multn, u, v as columns)
u
uu
u = 0 |u| = 0 u = 0
1
If u is non-zero, then |u| u is a unit vector
If S is an orthogonal set of nonzero vectors, then S
is linearly indepen
Use of Electronic Calculators during Semester 1 AY11/12 Examinations
1. The general rules on the use of electronic calculators are found from the Registrars Office
exam directory for students at https:/inetapps.nus.edu.sg/registrar/exam/students.html
unde
ST1131 Introduction to Statistics
DSAP
Solution
Tutorial 3
Lecture 5
Lecture 6
1.
: Association: Contingency, Correlation, and Regression
: Gathering Data
(3.6) How to fight terrorism?
A survey of 1000 adult Americans (Rasmussen Reports, April15, 2004) as
ST1131 Introduction to Statistics
DSAP
Solution
Tutorial 9
1.
(10.2) Sampling Sleep:
The 2002 Sleep in America poll of 1010 adults reported that respondents slept an
average of 6.9 hours on weekdays and 7.5 hours on weekends, and that 30% of
respondents g
ST1131 Introduction to Statistics
DSAP
Solution
Tutorial 4
Lecture 7 & 8 : Probability in Our Daily Lives
1.
(5.6) Random Digits:
Consider a random number generator designed for equally likely outcomes. Which of the
following is not correct, and why?
a. F
ST1131 Introduction to Statistics
DSAP
Solution
Tutorial 1
Lecture 1: Introduction to Statistics & Displays of Categorical Data
Lecture 2: Displays of Quantitative Data & Shapes of Distributions
1.
(1.24) UW student survey:
a. The population is 40858 memb
ST1131 Introduction to Statistics
DSAP
HW2
1.
(2.40) Net worth by degree:
Statistical Abstract of the United States 2000 reported that in 1998 for those with a
college education, the median net worth was $146,400 and the mean net worth was
$528,200. For t
N ATIONAL UNIVERSITY O F S INGAPORE
EXAMINATION
STl131
INTRODUCTION T O S TATISTICS
(Semester 1: A Y 2010-2011)
Nov 2010 - Time Allowed: 2 Hours
INSTRUCTIONS T O C ANDIDATES
1.
, .)
This examination paper contains F OUR (4) questions and comprises (1
ST1131 Introduction to Statistics
Instructor: Li Jialiang, S16/07-111, 6516-8932, stalj@nus.edu.sg
Time & Place: Wednesday & Friday 10am 12pm, LT26
Office Hours: Wednesday & Friday 2pm 3pm or by appointment
Summary: This module introduces students to the