The Hong Kong Polytechnic University
Department of Applied Mathematics
AMA1006 Basic Statistics
Semester 2, 2014/2015
Lectures: Tuesday, 10:30-12:20 for weeks 1,2,5,6,9,10, and 11; 10:30-11:20 for weeks
3,4,7,8, and 13. No lecture in week 12 (thanks to Th

Topic
T i 3
Sampling Distribution and
p g
Estimation
Section 1 Estimation
Section 1.1 Point Estimate
Statistical inference enables us to make judgments about a
population on the basis of sample information
information.
The mean, standard deviation, and pr

Table of the Standardized Normal Distribution
P
The table gives the probability
P = Pr(Z > z )
0
where Z ~ N(0,1).
z
z
0.0
0.1
0.2
0.3
0.4
.00
0.5000
0.4602
0.4207
0.3821
0.3446
.01
0.4960
0.4562
0.4168
0.3783
0.3409
.02
0.4920
0.4522
0.4129
0.3745
0.3372

Q2. Let X N(2, 102 ). Find the constants a, b, and c, such that P (X > a) = 0.3, P (X
b) = 0.6, and P (c X 0) = 0.2.
Solutions. We let Z =
X2
10
to have Z N(0, 1).
(1). 0.3 = P (X > a) = P Z >
(2). 0.6 = P (X b) = P Z
b2
= 0.25, so b = 4.5.
10
a2
10
b2

AMA 1006 - Assignment 2
1. Let X be a random variable with the following probability distribution:
x
-2
3
5
f (x)
0.3
0.2
0.5
Find the standard deviation of X.
2. The random variable X, representing the number of errors per 100 lines of software
code, has

Topic
T i 2
Probability Distribution
y
Section 1 Discrete Random Variable
Section 1.1 Probability Distribution
Definitions:
A random variable is a variable whose value is
determined by the outcome of a random experiment.
A random variable that assumes cou

Q1. Assume that X Binomial(300, 0.3). Find the following probabilities.
(a). P (27 X < 85)
(b). P (X = 88)
(c). P (X > 100)
(d). P (X 100)
Solutions. We have 300 0.3 = 90 > 5, 300 (1 0.3) = 210 > 5, and 300 0.3 0.7 = 63 so
approximately X N (90, 63). Let

AMA1006 Basic Statistics
Lecture 9
Xin GUO
Email: x.guo@polyu.edu.hk
Oce: TU825
Telephone: 3400 3751
Oce Hours: Friday 14:00-16:00
1 / 28
Review
Uniform distribution: X Uniform(a, b),
1
Density function: f(x) = ba for a < x < b.
for any a x1 < x2 b, P(x1

AMA1006 Basic Statistics
Lecture 9
Xin GUO
Email: x.guo@polyu.edu.hk
Oce: TU825
Telephone: 3400 3751
Oce Hours: Friday 14:00-16:00
1 / 28
Review
Uniform distribution: X Uniform(a, b),
1
Density function: f(x) = ba for a < x < b.
for any a x1 < x2 b, P(x1

AMA1006 BASIC STATISTICS, SUPPLEMENTARY PROBLEMS
Part 3, Sampling Distribution and Estimation
Note: in this set of problems the words nd, estimate, etc., sometimes mean approximate.
We hope students to decide the trade-o between precision and computation

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TM 2N Bcrvonu‘aliﬂal 0.7).
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AMA 1006 Exercise 3
1. Dene suitable populations from which the following samples are selected:
(a) Persons in 200 homes are called by telephone in the city of Richmond and asked
to name the candidate that they favor for election to the school board.
(b)

c. If P (A B) = 0.1, what is P (A B)?
(25). Suppose A and B are two events with P (A B) = 0.8 and P (A B) = 0.2.
a. Find the possible range of P (A).
b. If P (A) = 0.6, what is P (B)?
(26). Suppose A and B are two events with P (A) = 0.6 and P (B) = 0.7.

AMA1006 Basic Statistics
Lecture 10
Xin GUO
Email: x.guo@polyu.edu.hk
Oce: TU825
Telephone: 3400 3751
Oce Hours: Friday 14:00-16:00
1 / 29
Review
Sampling Distribution of X
mean
standard error
Distribution
Normal Population Other Population
N(, 2 )
with ,

Q1. Assume that X Binomial(300, 0.3). Find the following
probabilities.
(a). P (27 X < 85)
(b). P (X = 88)
(c). P (X > 100)
(d). P (X 100)
1
Q2. Let X N (2, 102). Find the constants a, b, and c, such that
P (X > a) = 0.3, P (X b) = 0.6, and P (c X 0) = 0.

Topic 1
Probability
Section 1 Experiments and Sample Space
Definitions:
An experiment is defined to be any process which
generates well defined outcomes. By this we mean that on
any single repetition of the experiment one and only one
of the possible expe

Q1. An experiment consists of ipping a coin three times and each
time noting whether it lands heads or tails.
(a). What is the sample space of this experiment?
(b). What is the event that tails occur more often than heads?
Solution. Let us use H to denote

Q1. A group of 5 girls and 4 boys is randomly lined up.
(a). What is the probability that the person in the second position is a boy?
(b). What is the probability that Tom (one of the boys) is in the
second position?
1
Q2. Let S = cfw_1, 2, 3, 4, 5, 6, A

Q1. A group of 5 girls and 4 boys is randomly lined up.
(a). What is the probability that the person in the second position is a boy?
(b). What is the probability that Tom (one of the boys) is in the
second position?
Solution. (a). If we ll the second pos

AMA1006 Assignment 1
1. To test the quality of a shipment of crystal glasses, we selected 50 glasses at random.
We found that one was scratched and chipped, three had only scratches, and two were
only chipped. Consider the following events: A is a chipped

Q1. We keep rolling two dice together until obtaining at least one
dice at 6. Find the probability that we roll exactly n rounds.
1
Q2. A drunk man takes a ring of n keys, where only one can open
the door of his home. Since drunk, he has no idea about the

Q1. We keep rolling two dice together until obtaining at least one dice at 6. Find the
probability that we roll exactly n rounds.
Solution. Let X be the number of rounds we roll to get at least one dice at 6. Since for each trial,
the probability that at