Q1. Screws produced by a certain company
will be defective with a probability 0.01 independently of each other.
The company sells the screws in packages of
10 and oers a money-back guarantee that at
m
MATH1853 (Part II) - Tutorial class 1
Sets and Integration
F. Tsang
October 24, 2017
University of Hong Kong
Information
Tutor: Fai Lung Tsang
Office: Room 316 Run Run Shaw Building
Contact hours: Thu
THE UNIVERSITY OF HONG KONG
MAY 2014 EXAMINATION
MATHEMATICS: PAPER MATH1853
Part I: Linear Algebra
1. (18 Points) Find the values of x, y and z that minimize 3x2 +2y 2 +z 2 +4xy+4yz
under the constra
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853: Linear Algebra, Probability and Statistics
May 15, 2015
9:30a.m.12:30p.m.
Only approved calculators as announced by the Examinations Sec
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853 LINEAR ALGEBRA, PROBABILITY AND STATISTICS
December 10, 2015
(9:30am - 12:30pm)
No calculators are allowed in this examination.
Answer AL
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853: LINEAR ALGEBRA, PROBABILITY AND STATISTICS
May 13, 2016
9:30AM-12:30PM
No calculators are allowed in this examination.
Answer ALL 7 ques
True/False Questions
System of linear equations
If a system of linear equations has two different
solutions, it must have infinitely many solutions
If
a11 x1 a12 x2
a1n xn
b1
a21 x1 a22 x2
a2 n xn
b
Matrices
As seen in the previous chapter, a matrix consists of vectors as
columns: A=[a1 a2 an]
For an mn matrix, its structure is
Two matrices are equal iff they have the same size and their
correspo
AS/1853/MATH1853/3
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Assignment 3 The Family of Bernoulli Related Distributions
Due Date: 3 December 2012 (17:00)
Please submit your assignment
AS/MATH1853/1
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Tutorial 2
1. Reduce the following quantity to a real number:
1 + 2i 2 i
+
.
3 4i
5i
2. (a) Establish the identity
1 + z + z2 +
AS/1853/MATH1853/1
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Assignment 1 Complex Numbers and Combinations
Due Date: 19 November 2012 (17:00)
Please submit your assignment to the assi
AS/1853/MATH1853/2
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Assignment 2 Probability
Due Date: 26 November 2012 (17:00)
Please submit your assignment to the assignment box (4/F, Run
AS/2603/MATH1853/1
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Assignment 4 (Normal Distribution and Statistical Inference)
Due Date: 10 Dec. 2012 (17:00)
Please submit your assignment
TUT/1853/MATH1853/1
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Tutorial 1
1. Demo. Let A = cfw_1, 2 and B = cfw_1, 3, 5, 6, 7.
(a) What are |A| and |B|?
(b) Find A B.
(c) Find A B.
(d)
3
Complex Variables
The imaginary number 1 i is a solution of the equation:
x2 + 1 = 0.
This idea of i was introduced to answer the above question. But then it results
in many interesting results, be
Q1. Let A = cfw_1, 2 and B = cfw_1, 3, 5, 6, 7.
(a) What are |A| and |B|?
(b) Find A B.
(c) Find A B.
(d) Write down all the subsets of A.
Answer. (a) |A| = 2 and |B| = 5.
(b)
A B = cfw_1 .
(c)
A B =
Q1. Andrew, Beatrix and Charles are playing
with a crown. If Andrew has the crown, he
throws it to Charles. If Beatrix has the crown,
she throws it to Andrew or to Charles, with
equal probabilities. I
Q1. Let z = 1 + i. Find |z| and Arg(z).
Answer.
|z| =
12 + 12 =
2 .
and
Arg(z) = tan1
1
= .
1
4
1
Q2. Verify that each of the two numbers
z = 1 3i
satises the equation
z 2 2z + 4 = 0 .
Answer. If z =
3
Complex Variables
The imaginary number 1 i is a solution of the equation:
x2 + 1 = 0.
This idea of i was introduced to answer the above question. But then it results
in many interesting results, be
#include <iostream>
using namespace std;
int main() cfw_
int width;
int height;
cout<"width: height: ";
cin>width>height;
for (int i=1;i<=height;i+)
cfw_
cfw_
for (int k=1;k<=i;k+)
cfw_
cout<"1";
if (
#include <iostream>
using namespace std;
int main() cfw_
int input;
cout<"height: ";
cin>input;
int width=input;
int height=input;
for (int i=1;i<=height;i+)
cfw_
cfw_
for (int k=2;k<=i;k+)
cfw_
cout<
MATH1853 Assignment 1 (Linear Algebra) Due: 18 Oct 2013 (Fri) HKT 5pm.
(Full mark is 115%. Please submit neat handwritten/typeset hardcopy to Engineering Faculty
Office reception counter at Haking Won
True/False Questions
System of linear equations
If a system of linear equations has two different
solutions, it must have infinitely many solutions
If
a11 x1 + a12 x2 + " + a1n xn = b1
a x + a x + "
MATH1853 II T7
Normal distributions
F. Tsang
University of Hong Kong
April 29, 2016
F. Tsang (University of Hong Kong)
MATH1853 II T7
April 29, 2016
1 / 14
3 things
Using the Standard normal table
Bin
Math1853, Probability theory essence
FLT
A sample space means:
Discrete case
A countable set S, and
a function P : S [0, ), fulfilling
P
xS
P (x) = 1;
or, Continuous case
An uncountable set S, and
The University of Hong Kong, Faculty of Engineering
MATH1853 Linear algebra, probability and statistics
(Academic Year 2012-13; 2nd Semester)
Linear Algebra Assignment 1 (by Dr. Ngai WONG)
1
1.
2.
a b