Chapter 6
Estimation
6.1
Point Estimation
Consider random variables for which the functional form of the PMF or PDF is known
but the distribution depends on an unknown parameter (say ) that may have any value
in a set (say ) called the parameter space.
Chapter 1
Probability
1.1
Basic Concepts
Background Reading: This section deals with the basic concepts of probability.
You must read this section (pp 111) in the first week of semester.
1.2
Properties of Probability
Background Reading: Read pp 1113 for a
MTH2232 Mathematical Statistics
1
Tutorial 05 Solution Set
Problems to be submitted at the start of your tutorial
1.
[HT5.1-2]
Here x =
y, Dy (x) =
g(y) = f
1
2 y
and 0 < x < maps onto 0 < y < . Thus
( ) 1 1 y/2
y = e
,
2 y
2
0 < y < .
Problems discussed
Chapter 3
Continuous Distributions
3.1
Continuous-type Data
[HT Example 3.1-1] The weights in grams of 40 miniature Baby Ruth candy bars, with
the weights ordered, are given below.
20.5
22.6
23.6
24.9
20.7
22.6
23.6
24.9
20.8
22.7
23.6
25.1
21.0
22.7
23.
Chapter 2
Discrete Distributions
2.1
Random Variables of the Discrete Type
f (x) = P(X = x) is the probability mass function of the random variable X.
A probability mass function must satisfy the following properties:
f (x) 0, for all xs in R
f (x) >
Chapter 5
Distributions of Functions of Random
Variables
5.1
Functions of One Random Variable
Let X be a continuous-type random variable with PDF f (x). Let u be a continuous
strictly monotone function with inverse function v. Then the probability densit
19, " Tr z
Mush = \(La wt 2&7 n 1
-% m(11) :th (e) g gut-M)
(n 049 =0 R UM. mawmum.
dB ,. z
drum) - L72 3w) = o
T d 9- 1(9 ) in
L -L n X? z
29 4 29" EA 0
@= n i. 2
lg Eb: M:
: Xi'M
0= 4n- Urn-M)
gyw gin-mu?
n = (72 z
Hm'hw'f) HR 7W)
: g"; X? = 0.7.
Were
MTH2232 Mathematical Statistics
1
Tutorial 04 Solution Set
Problems to be submitted at the start of your tutorial
1.
[HT4.2-12]
The marginal distributions of X and Y are, respectively,
1
fX (x) =
8xydy = 4x(1 x2 ), 0 x 1,
x y
8xydx = 4y 3 , 0 y 1.
fY (y)
Chapter 4
Bivariate Distributions
4.1
Distributions of Two Random Variables
Let X and Y be two random variables defined on a discrete probability space. The
probability that X = x and Y = y is denoted by f (x, y) = P(X = x, Y = y). The
function f (x, y)
MONASH UNIVERSITY
SCHOOL OF MATHEMATICAL SCIENCES
MAT2003 Continuous Mathematics for Computer Science
Mathematics Laboratory 1
(Week 2)
The more problems you have solved, the more likely it is that you will be able to solve the next one.
Doing mathematics
MONASH UNIVERSITY
SCHOOL OF MATHEMATICAL SCIENCES
MAT2003 Continuous Mathematics for Computer Science
Mathematics Laboratory 1
(Week 2)
SOLUTIONS
The more problems you have solved, the more likely it is that you will be able to solve the next one.
Doing m
COST ACCOUNTING Chapter 3
Kelompok : Accounting 3B
Aldo Santos
0134141005
Devi Ratnadhani
0134141046
Chyntia Octavia
0134141012
Hansel Addison
0134141029
PROBLEM 3-40
a. Biaya service komputer perusahaan - Mixed cost, karena ada biaya tetap sebesar $150 d
MTH2032 Differential Equations with Modelling
Problem Set 3
School of Mathematical Sciences, Monash University
These problems cover the work from week 3. Students are strongly advised to work through all
the problems either privately or in support classes
MTH2032 Differential Equations with Modelling
Problem Set 2
School of Mathematical Sciences, Monash University
These problems cover the work from week 2. Students are strongly advised to work through all
the problems either privately or in support classes
MTH2032 Differential Equations with Modelling
Problem Set 4
School of Mathematical Sciences, Monash University
These problems cover the work from week 4. Students are strongly advised to work through all
the problems either privately or in support classes
MTH2032 Differential Equations with Modelling
Problem Set 6
School of Mathematical Sciences, Monash University
These problems cover the work from week 6. Students are strongly advised to work through all
the problems either privately or in support classes
MTH2032 Differential Equations with Modelling
Problem Set 1
School of Mathematical Sciences, Monash University
These problems cover the work from week 1. Students are strongly advised to work through all
the problems either privately or in support classes
MTH2032 Differential Equations with Modelling
Problem Set 5
School of Mathematical Sciences, Monash University
These problems cover the work from week 5. Students are strongly advised to work through all
the problems either privately or in support classes
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 10
School of Mathematical Sciences, Monash University
These problems cover the work from Week 10, and will be discussed in support classes during Week 11. Problems mark
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 12
School of Mathematical Sciences, Monash University
These problems cover the work from Week 12.
1.
Let Q be an m n matrix with orthonormal columns (with respect to th
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 8
School of Mathematical Sciences, Monash University
These problems cover the work from Week 8, and will be discussed in support classes during Week 9. Problems marked
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 11
School of Mathematical Sciences, Monash University
These problems cover the work from Week 11, and will be discussed in support classes during Week 12. Problems mark
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 9
School of Mathematical Sciences, Monash University
These problems cover the work from Week 9, and will be discussed in support classes during Week 10. Problems marked
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 5
School of Mathematical Sciences, Monash University
These problems cover the work from Week 5, and will be discussed in support classes during Week 6. Problems marked
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 4
School of Mathematical Sciences, Monash University
These problems cover the work from Week 4, and will be discussed in support classes during Week 5. Problems marked
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 1
School of Mathematical Sciences, Monash University
These problems cover the work from Week 1, and will be discussed in support classes during Week 2. Problems marked
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 7
School of Mathematical Sciences, Monash University
These problems cover the work from Week 7, and will be discussed in support classes during Week 8. Problems marked
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 3
School of Mathematical Sciences, Monash University
These problems cover the work from Week 3, and will be discussed in support classes during Week 4. Problems marked