Assignment 4: Probability Density
Question 1 (exercise 9 of chapter 5):
cos x 0 x 2
.
Let the phase error in a tracking device have probability density f(x) =
0
elsewhere
Find the probabilities that
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
In
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 mod
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,
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
(E
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
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 chapte
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
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
In
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
Inf
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
Tutorial 5
Probability Density 3
ENGG2450B Tutors
The Chinese University of Hong Kong
8 March 2016
1/7
Expected Value
2/7
Expected Value
Consider a function g (X ) of a single random variable X . The
THE CHINESE UNIVERSITY OF HONG KONG
Department of Electronic Engineering
ENGG2450B Probability and Statistics for Engineers
Assignment 7: Inferences concerning a mean
Deadline: 11:30 a.m. March 30, 20
THE CHINESE UNIVERSITY OF HONG KONG
Department of Electronic Engineering
ENGG2450B Probability and Statistics for Engineers
Assignment 9: Inferences Concerning Variances
Deadline: 11:30 a.m. April 13,
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
In
5 Probability densities
5.1 Continuous random variables
5.2 The normal distribution
5.3 The normal approximation to
the binomial distribution
5.5 The uniform distribution
5.10 Joint distribution discr
Assignment 7: Inferences concerning a mean
Question 1 (exercises 1 & 2 of chapter 7):
Civil engineers collected data from one area of a cold city on the amount of salt (tons) used to
keep highways dri
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
In
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
In
THE CHINESE UNIVERSITY OF HONG KONG
Department of Electronic Engineering
ENGG2450B Probability and Statistics for Engineers
Assignment 2: Probability and Probability Distribution
Deadline: 11:30 a.m.
THE CHINESE UNIVERSITY OF HONG KONG
Department of Electronic Engineering
ENGG2450B Probability and Statistics for Engineers
Assignment 10: Stationary and Ergodic Random Processes
Deadline: 11:30 a.m.
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
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 outcom
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
Choos
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
=
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 para
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 p