NAME
STUDENT #
York University
MATH 2030 3.00MW Elementary Probability
First Midterm Examination Solutions (Salisbury)
February 11, 2011
You have 50 minutes to complete this exam. There are 5 ques
MATH 2030 3.0MW (Elementary Probability)
Assignment 2 Solutions
January 2011 Salisbury
1.4 No. 4
(a) By independence, P (Ac B c ) = P (Ac )P (B c ) = (1 P (A)(1 P (B ) =
0.9 0.7 = 0.63
(b) A B = (Ac B
York University
MATH 2030 3.0MW (Elementary Probability)
Assignment 3 Solutions
February 2011 Salisbury
1.5 No. 3
(a) We test a chip. Let B be the event that the chip is good, so B c is the event
that
York University
MATH 2030 3.0MW (Elementary Probability)
Assignment 4 Solutions
February 2011 Salisbury
3.1 No. 9
X = 2 if the 2nd draw matches the rst, which has probability 1 . X = 3 if the
7
2nd dr
York University
MATH 2030 3.0MW (Elementary Probability)
Assignment 4 Solutions
February 2011 Salisbury
3.1 No. 9
X = 2 if the 2nd draw matches the rst, which has probability 1 . X = 3 if the
7
2nd dr
York University
MATH 2030 3.0MW (Elementary Probability)
Assignment 5 Solutions
February 2011 Salisbury
2.1 No. 4
By the denition of conditional probability, and the independence of the rolls,
P (2 si
York University
MATH 2030 3.0MW (Elementary Probability)
Assignment 6 Solutions
March 2011 Salisbury
3.2 No. 5
(a) I dont think much of the argument. Write K for the number of times
the chosen number
York University
MATH 2030 3.0MW (Elementary Probability)
Assignment 7 Solutions
March 2011 Salisbury
3.3 No. 2
The distribution of Y is
y
0
1
2
3
P (Y = y ) 1/8 3/8 3/8 1/8
Recall that
E [g (Y )] = g
York University
MATH 2030 3.0MW (Elementary Probability)
Assignment 8 Solutions
April 2011 Salisbury
2.4 No. 4
(a) Let X be the number of days with thirty or more 6s. Then X Bin(n, p)
where n = 365 an
York University
MATH 2030 3.0MW (Elementary Probability)
Practice problems Solutions
April 2011 Salisbury
3.1 No. 2
(a) The following gives P (X = x, Y = y ) for sampling with replacement.
1
1
2
3
4
y
York University
Faculty of Science and Engineering
MATH 2030 3.00MW Elementary Probability
Instructor: T. Salisbury
Second Midterm Examination Solutions
March 18, 2011
NAME:
SIGNATURE:
STUDENT NUMBER:
York University
MATH 2030 3.0MW (Elementary Probability)
Assignment 1 Solutions (corrected)
January 2011 Salisbury
1.1 No. 2
(a) We use an equally likely outcomes model with
= cfw_suppose, a, word, i
MATH 2030 3.00MW Elementary Probability
Course Notes
Part V: Independence of Random Variables,
Law of Large Numbers,
Central Limit Theorem,
Poisson distribution
Geometric & Exponential distributions
T
York University MATH 2030 3.0AF (Elementary Probability) Midterm I - SOLUTIONS October 12, 2007 NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are 5 questions on 4 pages.
York University MATH 2030 3.0AF (Elementary Probability) Midterm Exam I SOLUTIONS October 17, 2008 NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are 4 pages, containing
York University MATH 2030 3.0AF (Elementary Probability) Midterm 1 Solutions October 4, 2006 Salisbury NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are ve questions, on
York University MATH 2030 3.0AF (Elementary Probability) Midterm 2 - Corrected Solutions November 7, 2007 NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are 5 pages, cont
York University MATH 2030 3.0AF (Elementary Probability) Midterm 2 October 30, 2006 Salisbury NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are four questions, on three
York University MATH 2030 3.0AF (Elementary Probability) Class Quiz SOLUTIONS September 26, 2008 NAME: STUDENT NUMBER: You have 20 minutes to complete the quiz. There are 2 pages, containing 2 questio
MATH 2030 3.00MW Elementary Probability
Course Notes
Part I: Models and Counting
Tom Salisbury [email protected]
York University
Winter 2010
Introduction [Jan 5]
Probability: the mathematics used for Stat
MATH 2030 3.00MW Elementary Probability
Course Notes
Part II: Independence and Conditional
Probabilities
Tom Salisbury [email protected]
York University
Winter 2010
Independence and Conditional Probabilit
MATH 2030 3.00MW Elementary Probability
Course Notes
Part III: Random Variables
Tom Salisbury [email protected]
York University
Winter 2010
Discrete Distributions [Jan 31]
Recall that a r.v. has a discret
MATH 2030 3.00MW Elementary Probability
Course Notes
Part IV: Binomial/Normal distributions
Mean and Variance
Tom Salisbury [email protected]
York University
Winter 2010
Binomial Distribution [Feb 14]
The
MATH 2030 3.00MW Elementary Probability
Course Notes
Part V: Independence of Random Variables,
Law of Large Numbers,
Central Limit Theorem,
Poisson distribution
Geometric & Exponential distributions
T