MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Homework Sheet 4
Due: Thursday 13th October: 2:30 PM
Basic Questions
1. What is the cumulative distribution function for the sum of two fair dice?
F (x) =
0
1
36
3
36
6
36
10
36
15
36
x<2
2
x<3
3
x<
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Homework Sheet 7
Due: Thursday 24th November: 2:30 PM
Basic Questions
1. If X is normally distributed with mean and variance 2 , and Y is exponentially distributed with parameter :
(a) Calculate the moment
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Homework Sheet 8
Due: Thursday 1st December: 2:30 PM
Basic Questions
1. Use Markovs inequality to obtain a bound on the probability that the product of two independent exponentially distributed random vari
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Sample Final Examination
This Sample Examination has more questions than the actual exam, in order
to cover a wider range of questions.
1. (a) A truncated standard normal random variable has probability de
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Homework Sheet 6
Due: Thursday 17th November: 2:30 PM
Basic Questions
1. If X is uniformly distributed on (0, 2) and Y is uniformly distributed on
(1, 3), what is the probability density function of X + Y
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Homework Sheet 5
Model Solutions
Basic Questions
1. Let X be normally distributed with mean 1 and standard deviation 1. What
is the probability that X 2 > 1?
X 2 > 1 if X > 1 or X < 1. Therefore P (X 2 > 1
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Homework Sheet 1
Model Solutions
Basic Questions
1. A statistics textbook has 8 chapters. Each chapter has 50 questions. How
many questions are there in total in the book?
8 50 = 400.
2. How many distinct
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Homework Sheet 2
Model Solutions
Basic Questions
1. For events A, B , C and D, how are the events (AB ) (CD) and (A
C )(B D) related?
The event (AB ) (CD) is a subset of the event (A C )(B D). It is easy
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Homework Sheet 3
Due: Thursday 6th October: 2:30 PM
Basic Questions
1. 4 fair coins are tossed. Which of the following pairs of events are independent?
There are exactly two heads
(a) The rst coin is a hea
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Sample Final Examination
This Sample Examination has more questions than the actual exam, in order
to cover a wider range of questions. The material from Chapters 15 is only
partially covered here. You sho