The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Apr 14, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Apr 20, 2015
Solution to Practice Problem 9
1. Since there are a large number of drivers, each of whom has a small probability of
being involved in an accident in a gi
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Apr 14, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Apr 20, 2015
Practice Problem 9
1. The number of trac accidents in Berkeley, California, in 10 randomly chosen nonrainy days in 1998 is as follows: 4, 0, 6, 5, 2, 1, 2
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Apr 27, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due May 4, 2015
Solution to Practice Problem 11
1. By Testing the Means of Two Samples with known Variances
H0 : 1 2 , H1 : 1 > 2
X Y
TS =
2
x /n
+
5.6 4.1
=
22 /9 + 22
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Apr 27, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due May 4, 2015
Practice Problem 11
1. The value received at a certain messagereceiving station is equal to the value sent
plus a random error which is normal, with mean
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
1 6
(A )
99/4
1 ( 15%)
(
)1. The part of statistics concerned with the drawing of conclusions from data is called
descriptive statistics ( ). Moreover, the part of statistics concerned with the
description and summarization of data is called inferential
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Engineering Probability and Statistics
Jiheng Zhang
Solution to Practice Problem 5
1. Let X denote the length of the call made by the person in the booth. Then the
desired probabilities are
P (X > 10) = 1 FX (10) =
1
e
P (10 < X < 20) = FX (20)
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Engineering Probability and Statistics
Jiheng Zhang
Solution to Practice Problem 4
1. (a)
M (t) = E[etX ]
n
etk
=
k=0
n
=
k=0
t
n k
p (1 p)nk
k
n
(pet )k (1 p)nk
k
= (pe + 1 p)n
(b) M (t) = n(pet + 1 p)n1 pet
M (t) = n(n 1)(pet + 1 p)n2 (pet )2
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Mar 31, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Apr 10, 2015
Solution to Practice Problem 7
1. (a) The summation of normal random variables to be a normal r.v., their is a
premise: independence. If we set Y = X, it
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Mar 31, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Apr 10, 2015
Solution to Practice Problem 8
1. (a) School A: xA = 83.708, xA = 87 and sA = 12.167.
School B: xB = 76.546, xB = 78 and sB = 12.459.
Since the sample mea
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Apr 27, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due May 4, 2015
Solution to Practice Problem 11
1. By Testing the Means of Two Samples with known Variances
H0 : 1 2 , H1 : 1 > 2
X Y
TS =
2
x /n
+
5.6 4.1
=
22 /9 + 22
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned May 4, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due May 8, 2015
Practice Problem 12
1. (a) Sxx = 334.1, SY Y = 19.3, SxY = 66.9, SS = 5.9
(b) y = 0.2x + 5.7
(c)
H0 : = 0; H1 : = 0
(n 2)Sxx
B = 4.3
SS
t/2,n2 = t0.025,8 =
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Apr 20, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Apr 24, 2015
Solution to Practice Problem 10
1. (a)
x t0.005,8 s/ 9 = 1.0056 (3.355)(0.0246/3) = 1.0056 0.0275
The 99% condence interval on the mean diameter is given
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Mar 16, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Mar 20, 2015
Practice Problem 6
1. First write out the Excel commands and then give the numerical answer for each
calculation.
(a) P cfw_
2
10
5 and
2
0.1,10
(b) P cf
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned May 5, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due May 8, 2015
Practice Problem 12
1. An electric utility wants to estimate the relationship between the daily summer temperature(degrees Fahrenheit) and the amount of ele
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Mar 23, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Mar 26, 2015
Practice Problem 7
1. (a) For independent standard random variables X and Y , we have X + Y
N (0, 2). However if we further set Y = X which gives Y N (0,
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
IELM 2510
Assigned April 11, 2017
Engineering Probability and Statistics
Songxiang Liu
Due April 19, 2017
Practice Problem 9
1. A certain component is critical to the operation of an electrical system and must be
replaced immediately upon failure. If the
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
L1: Introduction to Management
L2: Project Management
OM: management of processes used to design, supply,
Project characteristics: temporary, unique, progressive elaboration.
produce and deliver valuable goods and services. to
Key decisions: deciding whic
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
M ODULE VI:
H YPOTHESIS T ESTING
Jin Fang
Spring, 2017
Introduction
Test in a Normal Population
Testing the Equality of Means
Test in Bernoulli Population
Test in Poisson Population
Introduction
In the previous module, we want to estimate the value of unk
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
managing
sustainable global
supply chains
Framework and Best Practices
nbs.net
Prepared by
Dr. Stephen Brammer
Dr. Stefan Hoejmose
Dr. Andrew Millington
and NBS
Supply chain
disruptions can
be devastating
for operations
and share price.
Managing Sustainab
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
M ODULE V:
PARAMETER E STIMATION
Jin Fang
Spring, 2017
Introduction
Point Estimate
Evaluating Point Estimate
Interval Estimate Normal
Introduction
In the previous modules, we know information about the distribution of the
population:
yearly claim of a pol
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
M ODULE II A :
R ANDOM VARIABLES D ISCRETE
Jin Fang
Spring, 2017
Introduction
PMF & CDF
Expectation
Variance
Bernoulli
Binomial
Hypergeometric
Geometric
MGF
Introduction to Random Variables
What is a variable?
x + 200,
sin(),
Z
1
0
p
ydy
What is a random
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Apr 20, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Apr 24, 2015
Practice Problem 10
1. A machine produces metal pieces that are cylindrical in shape. A sample of these
pieces is taken and the diameters are found to be
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Feb 4, 2014
Engineering Probability and Statistics
Jiheng Zhang
Due Feb 6, 2014
Practice Problem 1
1. For each of the following experiments, describe the sample space.
(a) Toss a coin three times.
(b) Count the number of insectdamaged
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Feb 11, 2014
Engineering Probability and Statistics
Jiheng Zhang
Due Feb 13, 2014
Practice Problem 2
1. A coin is tossed three times. What is the probability that exactly two heads occur,
given that:
(a) the rst outcome is a head?
(b) t
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Feb 23, 2014
Engineering Probability and Statistics
Jiheng Zhang
Due Feb 27, 2014
Practice Problem 3
1. Roll two fair dice. Let X denote the result of the outcome of the rst dice subtract
the outcome of the second dice.
(a) What are the
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Mar 16, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Mar 20, 2015
Practice Problem 6
1. First write out the Excel commands and then give the numerical answer for each
calculation.
(a) P cfw_2 5 and 2
10
0.1,10
(b) P cfw_
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Mar 3, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Mar 6, 2015
Practice Problem 4
1. X is a Binomial random variable with parameters (n, p).
(a) Find the moment generating function of X.
n k nk
)
(Hint: (a + b)n = n
k=0
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2015
IELM 2510
Assigned Mar 9, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Mar 13, 2015
Practice Problem 5
1. Suppose that the length of a phone call in minutes is an exponential random variable
with parameter = 1/10. If someone arrives immedi