MATH1853 Linear Algebra, Probability and Statistics
Assignment 1 by Dr. N. Wong
Answer All questions which are from Final of 2013. Due on 23 Oct (Thu) 5pm,
please submit only HARDCOPIES, either neatly handwritten or typeset. Please
submit to the collectio

Fall 2013
MATH1853 (Linear Algebra)
Dr. N. Wong
Problem Set #1
1. Solve the following equations by Gaussian elimination.
2x1 + 3x2 + 11x3 + 5x4 = 2
x1 + x2 + 5x3 + 2x4 = 1
.
2x1 + x2 + 3x3 + 2x4 = 3
x1 + x2 + 3x3 + 4x4 = 3
2. When a and b are real numbe

TUT/1853/MATH1853/5
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Tutorial 5
1. It is known that screws produced by a certain company will be defective with a
probability 0.01 independently of each other. The company sells the screws in
packa

TUT/1853/MATH1853/4
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Tutorial 4
1. 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
Ch

TUT/1853/MATH1853/3
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Tutorial 3
1. Let 3 = 1 and = 1. Find the value of 2011 + 1997 + 1.
2. Show that tanh(ix) = i tan(x).
3. From a group of 5 women and 7 men, how many dierent committees of 2 wom

TUT/1853/MATH1853/2
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Tutorial 2
1. Let z = 1 + i. Find |z| and Arg(z).
2. Verify that each of the two numbers z = 1
3i satises the equation
z 2 2z + 4 = 0.
3. Reduce the following quantity to a re

AS/1853/MATH1853/4
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Assignment 4 (Normal Distribution and Statistical Inference)
Due Date: 29 Nov. 2014 (SAT) (17:00)
1. Let X follows the normal distribution N (1, 9). Find
(a) P (X 1.4). (b) P (X

AS/1853/MATH1853/2
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Assignment 2 Combinations and Probability
Due Date: 14 November 2014 (FRI) (17:00)
Please submit your assignment to the assignment box (4/F, Run Run Shaw Building)
1. In order t

AS/1853/MATH1853/3
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Assignment 3 The Family of Bernoulli Related Probability Distributions
Due Date: 21 November 2014 (FRI) (17:00)
Please submit your assignment to the assignment box (4/F, Run Run

TUT/1853/MATH1853/1
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853
Tutorial 1
1. 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.
2. Let A = cfw_x2 : x Z and

MATH 1853 Linear Algebra, Probability and Statistics
Instructor: Prof. Wai-Ki CHING
Room 414, Run Run Shaw Building, Email: wching@hku.hk.
Consultation Hours: TUE 09:30 - 11:30 and FRI 09:30 - 10:30.
Time Table: (A) 08:30-09:20 MON,TUE, FRI (LE4) and (B)

4
Permutations and Combinations
In this section, we introduce some symbols for counting combinations.
The symbol n! represents the product of all integers from 1 to n. In other words,
it means that
n! = n (n 1) (n 2) (n 3) 3 2 1.
For simplicity of discus

13
Bernoulli Experiment and Its Related Distributions
An experiment is called a Bernoulli experiment if there are only two possible
outcome: success with probability p and failure with probability (1 p) where
0 < p < 1.
We say X is a Bernoulli random vari

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, beautiful theory and useful applications.
In general a c

MATH1853 Maths I
Vectors
Dr. Ngai WONG
Fall 2014
1
Vectors
A real number is a point on the real line R
To describe a point on a plane R2, we use two numbers, e.g., (3,-1)
In fact, this is just an expression of a point using rectangular or
Cartesian coordi

MATH1853 Maths I
Matrix/Matrices
Dr. Ngai WONG
Fall 2014
1
Matrices
As seen in previous notes, 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
correspond