INSTRUCTIONS: Dictionaries and Scientic Calculators are allowed only. Question 1 ( marks 30). Dene (i)(marks 3) a random variable. (ii) (marks 9) a nite random variable and its distribution? Give an example. (iii) (marks 9) a discrete random variable in g
THE INTERNATIONAL UNIVERSITY(IU) - VIETNAM NATIONAL UNIVERSITY - HCMC
MIDTERM TEST Date: April, 2006 Duration: 90 minutes
SUBJECT: PROBABILITY AND STATISTICS Head of Department of Mathematics Signature: Full name: Prof. Phan Quoc Khanh
Lecturer: Signature
THE INTERNATIONAL UNIVERSITY - VIETNAM NATIONAL UNIVERSITY - HCMC
FINAL TEST Date: June 26, 2006 Duration: 90 minutes
SUBJECT: PROBABILITY AND STATISTICS (IT) Head of Department of Mathematics Signature: Full name: Prof. Phan Quoc Khanh
Lecturer: Signatur
FINAL EXAM FOR EE AND IT SCHOOLS INSTRUCTIONS: The following documents are allowed: Dictionaries, scientic calculators and copies of probability tables. Question 1.(20 marks). (a) Denition of a second order stochastic process ? (b) Denition of a weakly st
THI MN XC SUT THNG K
Thi gian lm bi:120 Cu 1. a. Gieo n con xc sc i xng v ng cht. tm xc st c tng s chm l n+1. b. Trung bnh trong 3 thng cui nm dng lch ma ln 5 ln.Tm xc sut khng c ngy no ma ln qu 1 ln. Cu 2: C 2 l sn phm: l I gm 6 chnh phm v 4 ph phm, l I
THI MN XC SUT THNG K
Thi gian lm bi:120 Cu 1. a. Tnh xc sut 12 ngi chn ngu nhin c ngy sinh ri vo 12 thng khc nhau. b. Thng k cc cp v chng mt vung cho thy:30% cc b v thng xem ti vi, 50% cc ng chng thng xem ti vi, xong nu v xem ti vi th 60% chng xem cng. L
THI MN XC SUT THNG K
Thi gian lm bi:120 Cu 1. a. Tn sut bch tng l 0,6 % vi nam v 0,36% vi n. Tm xc sut trong mt lng c s nam = s n ta gp c. 1. Trong lng 1 ngi b bnh bch tng. 2. Trong nhm bch tng mt ngi l nam. b. Sinh i ng trng th cng gii, khc trng th sc x
THI MN XC SUT THNG K
Thi gian lm bi:120 Cu 1. a. Ba thy thuc c xc sut chn bnh ng l 0,8:0,9:0,7.Tm xc sut sau khi chn bnh c 1 v ch 1 kt qu ng th l ca ngi th 3. b. Anh c 5% cha mt en khi con mt en v tng t 7,9% cha en-con xanh, 8,9% cha xanh con en, 78,2% c
P ROBLEMS FOR THE MIDDLE TERM EXAM
[1] Given three sets A, B, C . Use the Venn diagram to illustrate the following sets: A B C , A B B (C \ (A B ). [2] Let a card be selected from two ordinary packs of 52 cards. Denote A = cfw_the card is Diamonds or club
P ROBLEMS FOR THE MIDDLE TERM EXAM
[1] Given three sets A, B, C . Use the Venn diagram to illustrate the following sets: A B C , A B B (C \ (A B ). [2] Let a card be selected from two ordinary packs of 52 cards. Denote A = cfw_the card is Diamonds or club
INTERNATIONAL UNIVERSITY-NATIONAL UNIVERSITY HOCHIMINH CITY
DEPARTMENT OF MATHEMATICS
COURSE OUTLINE
for
INTRODUCTION TO PROBABILITY AND MATHEMATICAL STATISTICS FOR FIELD BIOLOGY AND MANAGEMENT
Course Code: No. of Credits: Instructor: Prof. Nguyen Van Thu
2.2. Wide-Sense Stationary (WSS) Processes
Mean of the random process X(t) is the mean of random variable X(t) at time instant t.
Autocorrelation function of X(t) is a function of two variables t1 = t and t2 = t + ,
E[ X (t )] = X (t )
Let fX(t)(x) be the
ELEMENTARY PROBABILITY AND STOCHASTIC PROCESSES
Nguyen Van Thu Professor Dr. HCMIU VN
1
SET THEORY
This Section treats some elementary ideas and concepts of set theory which are necessary for a modern introduction to probability theory. Any well dened
P ROBLEMS FOR THE MIDDLE TERM EXAM
[1] Given three sets A, B, C . Use the Venn diagram to illustrate the following sets: A B C , A B B (C \ (A B ). [2] Let a card be selected from two ordinary packs of 52 cards. Denote A = cfw_the card is Diamonds or club
REVIEW QUESTIONS FOR FINAL EXAM 12/08
A. Chapter 6: Some continuous probability distributions Q. 1 What is a normal distribution N (, 2 ) and a normal random variable? What is the standard normal distribution and the standard normal random variables? What
ELEMENTARY PROBABILITY AND STOCHASTIC PROCESSES
Nguyen Van Thu Professor Dr. HCMIU VN
1
SET THEORY
This Section treats some elementary ideas and concepts of set theory which are necessary for a modern introduction to probability theory. Any well dened
Chapter 11
Markov Chains
11.1 Introduction
Most of our study of probability has dealt with independent trials processes. These processes are the basis of classical probability theory and much of statistics. We have discussed two of the principal theorems
Dr. Michael Monticino University of North Texas Department of Mathematics
Oneofcentraladvancesofthe20th centurywas theunderstanding,quantificationandmasteryof uncertainty Withoutthetoolsofprobabilityand statistics,manyoftheadvancesinengineering andscience