o Herp Me Serve This )
b. New perform the same calculations for the data without the point (2.3). Remove the conesponding column
= uestion Hei
- Q p from the table and find sums.
Totals
a. Using the pairs of values for all 10 points. find
The two main branches
of calculus
BY MADDISON BAILEY
What is calculus?
the branch of mathematics that deals with the finding and properties of
derivatives and integrals of functions, by methods originally based on
the summation of infinitesimal difference
QUESTION 1.
(a) (i) State the Nested Interval Property.
(14 marks)
(3 marks)
Answer:
Suppose for n N, In = [an , bn ] is a sequence of closed intervals with
I0 I1 I2 In In+1 .
Then
nN In
is nonempty.
(2 marks)
(b) (i) State the denition of a set S is coun
Other questions adapted from 2011, 2012, Tests, Sample Tests,
etc, that are relevant to 2014/15 Test 1
QUESTION 1.
(a) State the Axiom of Completeness.
Answer:
Every nonempty subset of real numbers that is bounded above has a least upper
bound.
(b) State
For graders only
Question
1
2
3
Bonus
Total
QUESTION 1.
Marks
(14 marks)
4pt (a) Give a sequence of nested open intervals
I1 I2 I3
where the intersection
In is empty. You need not justify your answer.
n=1
+
Answer: For n N , let In = (0,
1
).
n
Then
In =
TEST 1 SAMPLE 2
For graders only
Question
1
2
3
Bonus
Total
QUESTION 1.
Marks
(14 marks)
(a) State the Nested Interval Property
Answer:
For each n N, let In = [an , bn ] be a closed interval. Suppose (In ) is a sequence
of nested intervals, i.e.,
I0 I1 I2
TOPIC 1/2
Question 1 (06-07)
(a) Explain the role played by Medisave, Medishield and Medifund in the financing of health
care in Singapore. What are the principal strengths and weaknesses of each?
(b) Do you foresee that the rising cost of health care wil
Chapter 9: Properties of Point Estimators and Methods of Estimation
9.1
Refer to Ex. 8.8 where the variances of the four estimators were calculated. Thus,
eff( 1 , 5 ) = 1/3
eff( 2 , 5 ) = 2/3
eff( 3 , 5 ) = 3/5.
9.2
a. The three estimators a unbias
Chapter 8: Estimation
8.1
Let B = B() . Then,
[
] [
]
(
)
[
2
MSE ( ) = E ( ) 2 = E ( E ( ) + B ) 2 = E E () + E ( B 2 ) + 2 B E E ()
= V ( ) + B 2 .
8.2
a. The estimator is unbiased if E( ) = . Thus, B( ) = 0.
b. E( ) = + 5.
8.3
a. Using Definition 8.3,
Chapter 7: Sampling Distributions and the Central Limit Theorem
7.1
a. c. Answers vary.
d. The histogram exhibits a mound shape. The sample mean should be close to 3.5 =
e. The standard deviation should be close to / 3 = 1.708/ 3 = .9860.
f. Very similar
Course Schedule for Econ modules offered in SEM 1, AY2014/2015
HE1001 Microeconomic Principles
HE1002 Macroeconomic Principles
HE1003 Basic Mathematics for Economists
HE204B/HE2005 Principles of Econometrics
HE206/HE2006 International Monetary Econom
SOLUTIONS TO PROBLEMS
C.1 (i) This is just a special case of what we Y covered in the text, with n = 4: E() = and
Var() = 2/4.
(ii) E(W) = E(Y1)/8 + E(Y2)/8 + E(Y3)/4 + E(Y4)/2 = [(1/8) + (1/8) + (1/4) + (1/2)] = (1 +
1 + 2 + 4)/8 = , which shows that W i