Independence
Wuhan University
September 21, 2012
Wuhan University
Independence
Conditional Probability I
The concept of probabilities of events are concerned with
questions of the following kind: If there are N balls in an urn, N1
white and N2 black, what

Tutorial 12
Question 1
(a)
A consumer welfare agency wants to investigate the relationship between the size
of houses and rents paid by tenants in a small town. The agency collected the
following information on the sizes (in hundred of square feet) of fiv

Chapter 8: Sampling Distribution
8.1 SAMPLING METHODS
1. Simple Random Sample
A simple random sample is a sample selected in such a way that every possible sample with the
same number of observation is equally likely to be chosen.
Assign a number to each

Chapter 7: CONTINUOUS PROBABILITY DISTRIBUTION
7.1 Probability Density Functions
The following requirements apply to a probability density function
a x b
f (x)
whose range is
.
1.
for all x between a and b
f ( x ) 0
2. The total area under the curve betwe

Tutorial 4
Question 1
a) A company wishes to review its distribution operation and from its time
sheet records it found that 144 vehicles were loaded in a 24 hour period. A
frequency distribution table was prepared from the data as follows:
Time to load (

Tutorial 10
Question 1
A study conducted a few years ago claims that adult men spend an average of 11 hours a week
watching sports on television with a standard deviation of 2.2 hours. A recent sample of 100
adult men showed that the mean time they spend

Chapter 6: Probability
6.1 Experiment, Outcome and Sample space
Random experiment
A random experiment is a process or course of action that results in one of a number of
possible outcomes. The outcome that occurs cannot be predicted with certainty.
Exampl

Tutorial 7
1. Hupper Corporation produces many types of soft drinks, including Orange Cola. The
filling machines are adjusted to pour 12 ounces of soda into each 12-ounce can of Orange
Cola. However, the actual amount of soda poured into each can is not e

Tutorial 1
1.
Compute the derivative of the given function and find the slope of the line that is tangent
to its graph for the specified value x. Hence, find the relevant equation of the tangent line for
the specified value of x = c.
(a) f(x) = 5x -3; x =

STA2203
CHAPTER 1: DIFFERENTIATION: BASIC CONCEPTS
1.1 The Derivative
Calculus is the mathematics of change, and the primary tool for studying change
is a procedure called differentiation.
Rates of Change and slope
y
(0, c)
=
x
x
# Rate of change is measu

Chapter 11: CHI-SQUARED TESTS
11.1: The Chi-square Distribution
The chi-square distribution has only one parameter, called the degrees of freedom. The shape of
a chi-square distribution curve is skewed to the right for small df and becomes symmetric for
l

CHAPTER 9: INTRODUCTION TO ESTIMATION
9.1 Concepts of Estimation
The objective of estimation is to determine the approximate value of a population parameter on
the basis of a sample statistic.
9.2 Estimating the Population Mean When The Population Standar

Chapter 12: Simple Linear Regression and Correlation
12.1 Describing the relationship between two variables
Statistics practitioners frequently need to know how two interval variables are related and
how strongly are they related.
A scatter diagram/Scatte

CHAPTER 2: INTEGRATION
2.1 The General Integration or Antiderivative of a Function
Algebraic Rules for Indefinite Integration
The constant multiple rule:
The sum rule:
kf x dx k f ( x)dx
f ( x) g ( x)dx f ( x)dx g ( x)dx
The difference rule:
f ( x)
g (

Tutorial 5
Question 1
Dinner bill amounts at ABC Restaurant have the following frequency distribution:
Dinner bill ($) Frequency
20 up to 30
2
30 up to 40
6
40 up to 50
8
50 up to 60
4
Find the
i)
Mean.
ii)
Median.
iii)
Mode.
iv)
Range.
v)
Variance and st

Tutorial 8
Question 1
(i)
The mean number of years of experience of a certain population of salespersons is 10
years. The standard deviation is 3 years. What is the probability that a random sample of
81 of these salespersons yields a mean greater than 10

Integration and Expectation
Wuhan University
September 28, 2012
Wuhan University
Integration and Expectation
Denition of Lebesgue Integration I
Let (, F, ) be a measure space( is not necessarily a nite
measure). We are going to dene the Lebesgue integrals

Probability Theory
Wuhan University
September 7, 2012
Wuhan University
Probability Theory
Introduction I
Probability theory is the mathematical analysis of random"
events, by which we mean outcomes of experiments, or
empirical phenomena with the following

Random variables
Wuhan University
September 7, 2012
Wuhan University
Random variables
Random variables I
Let (, F) be a measurable space, a function X : R is said
to be an F-measurable function or a random variable if
X 1 (B) := cfw_ : X () B F
for any Bo

V~K
2011c11 11F
1
1.
ln
=
k
n!
k!(n k)!
cfw_"d|, X
n
n k nk
x y
k
(x + y)n =
k=0
n
n
? k
n
k
O
r |1k| nk , K k
n
n1 n2 nr
=
n!
n1 !n2 ! nr !
cfw_"dX
(x1 + x2 + + xr )n =
n1 +n2 +nr =n
~ 1. b
kn / G
n
xn1 xn2 xnr
n1 n2 nr
ko
n1 , n2 , n3 , n4"XJcfw_

Conditional Expectation
Wuhan University
November 28, 2012
Wuhan University
Conditional Expectation
Finite Decomposition I
Let (, F, P) be a probability space. A collection of events
D = cfw_D1 , D2 , , DN
is called a non-trivial decomposition if
N
Dj ,

Probability Theory
Wuhan University
September 14, 2012
Wuhan University
Probability Theory
Introduction I
Probability theory is the mathematical analysis of random"
events, by which we mean outcomes of experiments, or
empirical phenomena with the followin

CHAPTER 10: INTRODUCTION TO HYPOTHESIS TESTING
10.1 Concepts of Hypothesis Testing
The null hypothesis refers to any hypothesis we wish to test and is denoted by H0.
The rejection of H0 leads to the acceptance of an alternative hypothesis, denoted by H1.

Chapter 5: Numerical Descriptive Measures
5.1: Measures of Central Tendency for Ungroup Data (mean, mode, median)
5.1.1 The Arithmetic Mean
The arithmetic mean is the sum of all the observations divided by the number of observations. It
is written in stat

Tutorial 6
a)
Question 1
Suppose that the following contingency table was set up:
A
B
C
10
20
D
15
25
Find
i)
ii)
iii)
iv)
P(A or C)
P(B and D)
P( B/C)
Are the event A and C independent? Are they mutually exclusive?
Why or why not.
Question 2
a) A market

Tutorial 2
1. Find the indicated integral
(a)
(y = -3x+c)
3 dx
(b)
(y = x6/6 +c)
x
(c)
5
dx
(y = 4
2
dt
t
(d)
(3t
(e)
2
(y = t3-
5t 2) dt
2 5 3/ 2
t 2t c)
3
(y = ex/2+
x
e
( 2 x x )dx
(f)
(g)
+c)
t
(y =
t
2
(e 1) dt
1/ 2
2
t (t t 2) dt
(y =
2. Solve the

FINANCING IN INTERNATIONAL
SETTLEMENT , CERTIFICATE OF
ORIGIN
Hanane
Amjad
Benjamin
INTRODUCTION
1.Export Finance
2.Import Finance
3.Innovation in international trade finance
4.Certificate of origin
INTRODUCTION
Financing means providing facilities of fun