Chapter 5
Integration
1
Introduction
Two distinct interpretations
Procedure which is the inverse of
differentiation
A method of determining the area under
the curve.
2
The process of finding the function when
its derivative is given is called integration
Chapter 7
Forecasting with
Exponential Smoothing
1
Forecasting Situation
Quantitative methods is part of
statistical studies which always involve
decision making.
If you have two or more options, you
have to choose the best option.
You have to make the
Chapter 8
Depreciation Methods
1
Introduction
Let us assume that you buy a car. The
very minute the car is driven out of the
sellers premises, the car starts to lose
its value.
Your car loses some value each time you
drive until the car stops running an
LECTURE 6
Applications of Calculus
1
Introduction
Calculus is used extensively in business
and economics. For instance, a company
may want to maximize profit, maximize
revenue or minimize cost.
An enterprise may want to determine the
best price for its
Chapter 4
Differentiation
1
Introduction
The management of a company may
want to measure the effect of price
change on the demand of their products.
The management can do this by using
derivatives to measure the decrease or
increase in demand when the p
BB202 Business Mathematics
Tutorial 6 Differentiation and Integration
1.
Differentiate the following with respect to
(a) 2 7 x
(b) x 2 x 3
(c) 3 x
2
2 2
x
3
(e) x 2 5 x 6
(d)
(f) x 2 x 2 3 x 3
2.
Find the indicated function if cost and revenue are given
BB202 Business Mathematics
Assignment (30%)
1.) This assignment should be done in a team of four students.
2.) This assignment has to be submitted in hard copy, either typed or hand written is acceptable.
3.) Show all necessary workings.
4.) Submission da
BB202 Business Mathematics
Tutorial 8 Exponential Smoothing
Q1
The Federal Election Commission maintains data showing the voting age
population, the number of registered voters, and the turnout for federal elections.
The following table shows the national
BB202 Business Mathematics
Tutorial 7 Application of calculus
1. The total revenue in euro per month of a product, R(x) is given by
R(x) = 40x 0.08x2, where x is the number of units produced and sold per
month. Find
(a) R(50)
(b) The average revenue funct
BB202 Business Mathematics
Tutorial 9 Depreciation Methods
Q1
A machine costing $30000 has a life expectancy of four years and zero salvage
value. Using the straight line method, calculate the annual depreciation.
Q2
A machine is purchased for $9000 in 20
Chapter 3
Index Numbers
1
Index Numbers
What is index numbers? Why do we need
an index number in decision making?
Why construction of index number might
change the conclusion of your final
decision?
An index number is a statistical measure
used to measu
Chapter 2
Mathematics of Finance I
Barnett/Ziegler/Byleen College Mathematics For Business, Economics,
Life Science, and Social Science 12e
1
Some Terms Used in Business Calculation
I = interest earned . Two basic types commonly
used: (i) Simple (ii) Com
Chapter 2
Mathematics of Finance II
Barnett/Ziegler/Byleen College Mathematics For Business, Economics,
Life Science, and Social Science 12e
1
Some Terms Used in Business Calculation
I = interest earned . Two basic types commonly
used: (i) Simple (ii) Co
Chapter 1 Business Equations
and Graphs II
1
MATRICES
2
MATRICES
3
TRANSPOSE MATRIX
Definition
The transpose of an matrix A, denoted
whose th row is the th column of .
AT, is the matrix
4
SPECIAL MATRICES
5
SPECIAL MATRICES
6
SPECIAL MATRICES
i <j .
7
MAT
BB202 Business Mathematics
Tutorial 4 Mathematics of Finance II
1. Goofy deposits $75 at the end of each quarter for 20 years into an account paying 4.8% annual interest
compounded quarterly.
a) How much is in the account at the end of 20 years?
b) How mu
BB202 Business Mathematics
Tutorial 5 Index Numbers
1.
The following tables show the sales of product over 5 years
Year
1
2
3
Sales
20
26
40
(RM000)
4
44
5
52
(a) Express the sales figures above as index numbers with year 1 as base year.
(b) Rebase your a
BB202 Business Mathematics
Tutorial 2 Business Equations and Graphs Part II
1.
Solve the matrix equation
(a)
2.
(b)
Let
Compute the indicated matrices:
(a)
(b)
(c)
3.
a)
Solve the equations below using Cramers rule.
x yz 4
x 2 y 3z 6
2x 3y z 7
b)
x yz 9
2
BB202 Business Mathematics
Tutorial 3 Mathematics of Finance I
1. If Simpson borrows $500 for 2 years from a bank that charges 6% annual simple interest, how much
interest will she owe at the end of the two years? How much (in total interest + principal)
BB202 Business Mathematics
Tutorial 1 Business Equations and Graphs I
1. Find the equation of the straight line that has the following properties:
(a)
(b)
Slope
and passes through
Passes through
and
.
.
2. Solve the following pairs of simultaneous equatio
AS 103 Statistics
Tutorial 5
1. Let X denote the number of auto accidents that occur in a city during a week. The
following table lists the probability distribution of X.
0
1
2
3
4
5
6
x
0.12
0.16
0.22
0.20
0.14
0.12
0.04
P( x)
(a) Determine the probabili
AS103 Statistics
Tutorial 6
1. The waiting time, in hours, between successive speeders spotted by a radar unit is a
continuous random variable with cumulative distribution
, x0
0
F ( x)
8 x
1 e , x 0
Find the probability of waiting less than 12 minutes b
AS103 Statistics
Assignment
Assignment 1 (10%)
1.) This is a group assignment. Each group should consist five/six students.
2.) This assignment has to be submitted in hard copy with a standardized cover page. The
assignment should be typed at 1.5 spacing
Extra Questions
1.
A continuous random variable X is uniformly distributed on [1, ] with mean 3.5.
(i)
(ii)
2.
Find the value of
(j14)
2
Find E ( X )
Suppose a randomly selected family has 3 children. Let random variable X be the number of sons
in a famil
AS 103 Statistics
CHAPTER 5
DISCRETE RANDOM VARIABLES
5.1
Random Variables
Definition
A random variable is a variable whose value is determined by the outcome
of a random experiment. In general, it is denoted by the capital letter, X.
Definition
A random
AS 103 Statistics
Chapter 6:
6.1
Continuous Random Variables
Continuous Probability Distribution
Definition 6.1.1
A continuous random variable is a random variable
whose values are not countable; it can assume any value over an interval or intervals.
For
AS 103 Statistics
CHAPTER 4
PROBABILITY
Random Experiment, Sample Space, Sample Point and Event
Definition
A random experiment is an experiment whose outcome cannot be
predicted with certainty.
Definition
The sample space S of an experiment is the set of