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ENGG2450B Quiz #5
Delete where appropriate
Tutor Name: Chen Yibo (Erb706) / Shen Yantao (YCLiang103) / Zhao Tianle (Erb405) *
Student Name: _
Student ID: _
Question: (Fill in the Blanks)
We use the sample mean X which is equal to
_
from a random sample

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ENGG2450B Quiz #4
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Tutor Name: Chen Yibo (Erb706) / Shen Yantao (YCLiang103) / Zhao Tianle (Erb405) *
Student Name: _
Student ID: _
Question:
A random sample consists of observations X , X , , X which are independent random varia

THE CHINESE UNIVERSITY OF HONG KONG
Department of Electronic Engineering
ENGG2450B Probability and Statistics for Engineers
Assignment 3: Probability Distribution
Deadline: 11:30 a.m. February 3, 2016
(Email the pdf file of your homework to [email protected]

ENGG2450 Probability and Statistics for Engineers
1
Introduction
3
Probabilityy
4
Probability distributions
5
Probability Densities
2
Organization and description of data
6
Sampling distributions
7
Inferences concerning a mean
8
C
Comparing
two treatments

Assignment 8: Comparing Two Treatments
Question 1 (exercise 10 of chapter 8):
As part of an industrial training program, some trainees are instructed by Method A, which is straight
computer-based instruction, and some are instructed by Method B, which als

ENGG2450 Probability and Statistics for Engineers
1
Introduction
3
Probabilityy
4
Probability distributions
5
Probability Densities
2
Organization and description of data
6
Sampling distributions
7
Inferences concerning a mean
8
C
Comparing
two treatments

ENGG2450 Probability and Statistics for Engineers
1
Introduction
3
Probability
4
Probability distributions
5
Probability Densities
2
Organization and description of data
6
Sampling distributions
7
Inferences concerning a mean
8
Comparing two treatments
9

ENGG2450B Probability and Statistics for Engineers
1 Introduction
3 Probabilityy
4 Probability distributions
5 Probability densities
2 Organization and description of data
6 Sampling distributions
7 Inferences concerning a mean
8 Comparing
C
two treatment

ENGG2450A Tutorial 6:
Continuous Random Variable
XU Tianrun
[email protected]
Quick Review
Independence
Covariance
Definition:
The covariance between two jointly distributed real-valued r.v.s X and Y with
finite second moments is defined as:
, = [( []

ENGG2450A Tutorial 7:
Description of Data & Sampling
XU Tianrun
[email protected]
Outlier
No rigorous definition
May have huge influence on our data analysis
How can we find the outliers?
Intuitive methods (plots,etc.)
Mathematical methods (Cooks distan

ENGG 2450A Probability and Statistics for
Engineers
SHAO, Shengcheng
27th Jan. 2016
SHAO, Shengcheng (CUHK)
ENGG 2450A Probability and Statistics for Engineers
27th Jan. 2016
1 / 14
Permutations
Choose r objects from n available distinct objects. Differen

Tutorial 4
Probability distribution
ENGG2450A zhouxiang
[email protected]
Geometric Distribution consider the number of the trials on which the first success
occurs.
, = (1 )1 , = 1,2,3
=
=1
=
(1 )1 = +
=
=1
so
1 =
=1
=1 (1
1 =+
1
=
1 ( + 1)

Test of Hypotheses
Related to decision making
Not just estimating the value of a parameter
Also decide whether a statement about the parameter
is true / false
Must test a hypotheses about the parameter
E.g. Quality control based on a random sample ma

ENGG2450A:
Probability and Statistics for Engineers
Tutorial 10
Wang Yunhan
Department of Systems Engineering and Engineering Management
CUHK
April 11, 2016
1 / 20
Tests of Hypotheses
There are many problems in which, rather than estimate the value of a
p

ENGG2450 Probability and Statistics for Engineers
1
Introduction
3
Probabilityy
4
Probability distributions
5
Probability Densities
2
Organization and description of data
6
Sampling distributions
7
Inferences concerning a mean
8
C
Comparing
two treatments

ENGG2450 Probability and Statistics for Engineers
1
Introduction
3
Probabilityy
4
Probability distributions
5
Probability Densities
2
Organization and description of data
6
Sampling distributions
7
Inferences concerning a mean
8
C
Comparing
two treatments

ENGG2450 Probability and Statistics for Engineers
1
Introduction
3
Probabilityy
4
Probability distributions
5
Probability Densities
2
Organization and description of data
6
Sampling distributions
7
Inferences concerning a mean
8
C
Comparing
two treatments

Assignment 10: Stationary and Ergodic Random Processes
Question 1:
Let the signals generated by two sources at a particular time be represented by two random
variables A and B. Suppose A and B are modulated to form a random process x(t) and
X(t) = A cos (

Assignment 3: Probability Distribution
Question 1 (exercise 44 of chapter 4):
Sln:
Chebyshevs theorem states that the tail probabilities P | X | k
1
and so the upper
k2
bounds are 1, and 1/9 for k=1, 2 and 3 respectively.
For binomial distribution,
=sqrt

THE CHINESE UNIVERSITY OF HONG KONG
Department of Electronic Engineering
ENGG2450B Probability and Statistics for Engineers
Assignment 8: Comparing Two Treatments
Deadline: 11:30 a.m. April 6, 2016
(Email the pdf file of your homework to [email protected]

THE CHINESE UNIVERSITY OF HONG KONG
ENGG2450A/B/C Probability and Statistics for Engineers
Mid-Term Examination
Instructions:
This paper must be answered in English. The duration of this paper is 1.5 hours.
Attempt ALL questions. The full marks of this

Assignment 5: Joint Distributions
Question 1 (exercise 72 of chapter 5):
(b) Find the probability that the second random variable is greater than the first.
Question 2 (exercises 76, 78 & 86 of chapter 5):
(a) P( 0.2< X <0.5, 0.4< Y <0.6)
(b)
(c)
(d)
(e)

Assignment 6: Sampling Distributions
Question 1 (exercise 10 of chapter 6):
Suppose that we convert the 50 samples referred to in the beginning of section 2 (slide 8 of Prb165C6Sampling-1.pdf) into 25 samples of size n=20 by combining the first two, the n

ENGG2450 Probability and Statistics for Engineers
1
Introduction
3
Probabilityy
4
Probability distributions
5
Probability Densities
2
Organization and description of data
6
Sampling distributions
7
Inferences concerning a mean
8
C
Comparing
two treatments

ENGG2450 Probability and Statistics for Engineers
1
Introduction
3
Probability
4
Probability distributions
5
Probability densities
2
Organization and description of data
6
Sampling distributions
7
Inferences concerning a mean
8
Comparing two treatments
9

Assignment 2: Probability and Probability Distribution
Question 1 (chapter 3 exercise 73):
A consulting firm rents cars from three agencies, 20% from agency D, 20% from agency E, 60% from
agency F. If 10% of the cars from D, 12% of the cars from E, and 4%

Assignment 9: Inferences Concerning Variances
Question 1 (exercise 8 of chapter 9):
If 12 determinations of the specific heat of iron have a standard deviation of 0.0086, test the null hypothesis that
=0.010 for such determinations. Use the alternative hy

Tutorial 1
Introduction
ENGG2450B Tutors
The Chinese University of Hong Kong
20 January 2016
1/7
Basic Concepts
2/7
Sample space
Definition
Sample Space. Sample Space is the set of all possible outcomes.
Sample space can be discrete or continuous.
E.G. Sa

ENGG2450B Quiz #6
*
Delete where appropriate
Tutor Name: Chen Yibo (Erb706) / Shen Yantao (YCLiang103) / Zhao Tianle (Erb405) *
Student Name: _
Student ID: _
Question:
A manufacturer claims that the thermal conductivity of a certain kind of its cement bri