MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 2
Model Solutions
Basic Questions
1. What is the probability that the sum of 3 fair 6-sided dice is 8?
The following possibilities sum to 8: (1,1,6), (1,2,5), (1,3,4), (1,4,3), (1,5,2),
(1,6

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 6
Due: Thursday 14th November: 2:30 PM
Basic Questions
1. X is normally distributed with mean 5 and standard deviation 1. Y is
independent and normally distributed with mean 2 and standard d

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 2
Due: Thursday 1st October: 2:30 PM
Basic Questions
1. What is the probability that the sum of 3 fair 6-sided dice is 8?
2. For an experiment with sample space cfw_1, 2, 3, 4, 5, is there a pro

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 7
Due: Thursday 21st November: 2:30 PM
Basic Questions
1. If X is exponentially distributed with parameter 1 and Y is exponentially
distributed with parameter 2 , where 2 > 1 :
(a) nd the mo

STAT 3360 - PROBABILITY
Midterm 1 - Tuesday October 19th - From 1:05 - 2:25 pm
Total Marks: 125 Marks
Dr. Ammar Sarhan
Name: Student ID: It is requested to answer all seven (7) questions.
Provide details of your working.
Please write legibly.
Anyone ca

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 4
Due: Thursday 10th October: 2:30 PM
Basic Questions
1. A random variable X has the following probability mass function:
x P (X = x)
0 0.1
1 0.2
3 0.3
4 0.2
7 0.1
20 0.1
(a) What is E(X)?
(

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 6
Model Solutions
Basic Questions
1. X is normally distributed with mean 5 and standard deviation 1. Y is
independent and normally distributed with mean 2 and standard deviation
3. What is P

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Sample Final Examination
This Sample examination has more questions than the actual nal, in order
to cover a wider range of questions. Estimated times are provided after each
question to help your preparat

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 1
Due: Thursday 19th September: 2:30 PM
Basic Questions
1. A statistics textbook has 10 chapters. Each chapter has 20 questions.
How many questions are there in total in the book?
2. How man

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 1
Model Solutions
Basic Questions
1. A statistics textbook has 10 chapters. Each chapter has 20 questions. How
many questions are there in total in the book?
There are 10 20 = 200 questions.

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Model Solutions
1. X is normally distributed with mean 2 and standard deviation 3. Y is
normally distributed with mean 4 and standard deviation 4. What is
P (Y > X )?
(a) If X and Y are independent?
If X a

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 2
Due: Thursday 26th September: 2:30 PM
Basic Questions
1. What is the probability that the sum of 3 fair 6-sided dice is 8?
2. For an experiment with sample space cfw_1, 2, 3, 4, 5, is ther

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 5
Due: Thursday 17th October: 2:30 PM
Basic Questions
1. If X is normally distributed with mean 0 and variance 1, what is the
probability density function of X 2 ?
2. Let X be normally distr

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 8
Due: Thursday 28th November: 2:30 PM
Basic Questions
Homework 7, Q. 1 If X is exponentially distributed with parameter 1 and Y is exponentially
distributed with parameter 2 , where 2 > 1 :

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 8
Due: Thursday 3rd December: 2:30 PM
Basic Questions
Homework 7, Q.1 If X is exponentially distributed with parameter and Y is normally
distributed with mean 0 and variance 2 ,
(b) Use the Cher

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 1
Due: Thursday 24th September: 2:30 PM
Basic Questions
1. A statistics textbook has 10 chapters. Each chapter has 20 questions and
each question has 3 parts. How many part-questions are there i

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 4
Due: Thursday 15th October: 2:30 PM
Basic Questions
1. A random variable X has the following probability mass function:
x P (X = x)
0 0.1
1 0.2
3 0.3
4 0.2
7 0.1
20 0.1
(a) What is E(X)?
(b) W

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 5
Due: Tuesday 27th October: 2:30 PM
Basic Questions
1. If X is normally distributed with mean 0 and variance 1, what is the
probability density function of X 2 ?
2. Let X be normally distribute

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 7
Due: Thursday 26th November: 2:30 PM
Basic Questions
1. If X is exponentially distributed with parameter and Y is normally
distributed with mean 0 and variance 2 ,
(a) nd the moment generating

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 1
Model Solutions
Basic Questions
1. A statistics textbook has 10 chapters. Each chapter has 20 questions and
each question has 3 parts. How many part-questions are there in total in
the book?
T

MATH/STAT 3360, Probability
FALL 2015 Hong Gu
Homework Sheet 2
Model Solutions
Basic Questions
1. What is the probability that the sum of 3 fair 6-sided dice is 8?
The following possibilities sum to 8: (1,1,6), (1,2,5), (1,3,4), (1,4,3), (1,5,2),
(1,6,1)

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 6
Due: Thursday 19th November: 2:30 PM
Basic Questions
1. X is normally distributed with mean 5 and standard deviation 1. Y is
independent and normally distributed with mean 2 and standard devia

MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 3
Due: Thursday 8th October: 2:30 PM
Basic Questions
1. Three fair dice are rolled. Which of the following pairs of events are
independent?
There is exactly one 6 among
(a) The rst roll is 6.
th

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Sample Midterm Examination
Model Solutions
This Sample Midterm has more questions than the actual midterm, in order
to cover a wider range of questions.
1. How many distinct ways can the letters of the wor

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 3
Model Solutions
Basic Questions
1. Three fair dice are rolled. Which of the following pairs of events are
independent?
There is exactly one 6 among
(a) The rst roll is 6.
the three rolls.

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 4
Model Solutions
Basic Questions
1. A random variable X has the following probability mass function:
x
0
1
3
4
7
20
P (X = x)
0.1
0.2
0.3
0.2
0.1
0.1
(a) What is E(X )?
E(X ) = 0.1 0 + 0.2

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 7
Model Solutions
Basic Questions
1. If X is exponentially distributed with parameter 1 and Y is exponentially
distributed with parameter 2 , where 2 > 1 :
(a) nd the moment generating funct

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 8
Model Solutions
Basic Questions
Homework 7, Q. 1 If X is exponentially distributed with parameter 1 and Y is exponentially
distributed with parameter 2 , where 2 > 1 :
(b) Use the Cherno b

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 5
Model Solutions
Basic Questions
1. If X is normally distributed with mean 0 and variance 1, what is the
probability density function of X 2 ?
The probability that X 2 < t is
1
2
x2
t
e 2

MATH/STAT 3360, Probability
FALL 2013
Toby Kenney
Homework Sheet 3
Due: Thursday 3rd October: 2:30 PM
Basic Questions
1. Three fair dice are rolled. Which of the following pairs of events are
independent?
There is exactly one 6 among
(a) The rst roll is 6