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 sma
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 n
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,
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
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 val
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 summe
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
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) =
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 Solution
1. (a) Possible values of X: cfw_5,4,3,2,1,0,1,2,3,4,5
(b)
P (X =
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 6
1. (a) =CHISQ.DIST(5,10,1) 0.109
=CHISQ.INV(0.9,10) 15.987
(b) =T.DIST(3,10,1) 0.993
=T.INV(0.9,10) 1.372
(
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.,
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
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
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 th
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 :
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
T
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
Practice Problem 8
1. A useful way of comparing two data sets is to put their stemandleaf plots s
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 va
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 devasta
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 th
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
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
IELM 2510
Assigned Mar 22, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Apr 4, 2015
Solution to Practice Problem 7
1. From the original table, we can obtain the following one:
X1 = i\X
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
IELM 2510
Spring 2017
Engineering Probability and Statistics
Songxiang Liu
Due Feb 13, 2017
Homework #1
1. For each of the following experiments, describe the sample space.
(a) Toss a coin three times
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
IELM 2510
Assigned Mar 24, 2015
Engineering Probability and Statistics
Jiheng Zhang
Due Apr 5, 2015
Practice Problem 7
1. The joint PMF of X1 and X2 is given in the following table.
X1 \X2
0
1
2
3
1
2
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
IELM 2510
Practice Problems
1. Random variable X N (0, 1):
(a) Find the probability density function of eX .
(b) Find EX.
(c) Find E[X 4 ].
2. Let X be the number of balls in a bin and X P oisson(1)
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
IELM 2510
Assigned May 8, 2014
Engineering Probability and Statistics
Jiheng Zhang
Due April 3, 2014
Homework #9
1. A chemical experiment has outcome A with probability p and B with probability
1 p. N
The Hong Kong University of Science and Technology
Engineering Probability and Statistics
IELM 2510

Spring 2014
Forecasting of ARCH Models Fitting of ARCH Models Extensions of ARCH Models
Outline
Forecasting of ARCH Models
Fitting of ARCH Models
Determine the Order of ARCH Models
Fitting of ARCH Models
Model Ch
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 t
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 co
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