MATH 331 sec002 Fall 2016 Quiz 1 Instructor: Dr. Brown
1. We roll a fair die. Let A be the event that the rolled number is even, and B the event that
the rolled number is divisible by 3. Express the event that we rolled a 3 using A and B.
Solution:
Our sa
MATH 331 sec002 Fall 2016 Homework 1 Instructor: Dr. Brown
1. Suppose a family contains two children of different ages, and we are interested in the gender
of these children. Let F denote that a child is female and M that the child is male and let
a pair
MATH 331 sec002 Fall 2016 Special Quiz
Instructor: Dr. Brown
1. (20 points)
Make all of the following computations.
Let X have density function f (x) = kx4 for x 1 and zero otherwise.
(a) Find k such that f (x) is a valid p.d.f.
Solution:
For f (x) to be
MATH 331 Fall 2016 Exam 2
Instructor: Dr. Isabelle Brown
Directions:
You must show your work to get credit for your solutions. Partial credit will be awarded.
Make sure to CLEARLY define any random variables or events you introduce, and remember
to spec
MATH 331 sec002 Fall 2016 Homework 4 Instructor: Dr. Brown
1. We have an urn with three green balls and two yellow balls. We pick a sample of two
without replacement and put these two balls in a second urn that was previously empty.
Next we sample two bal
Math 431
Exam 1 (with answers)
Spring 2012
1. A fair die is rolled 20 times.
(a) [3 points] What is the probability of 3 sixes in the first twenty rolls?
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
Solution: Using the binomial distribu
MATH 331 sec002 Fall 2016 Homework 2 Instructor: Dr. Brown
1. We roll a fair die repeatedly until we see the number four appear and then we stop.
a. Following an example discussed in class, describe a sample space and a probability
measure P to model this
MATH 331 sec002 Fall 2016 Homework 3 Instructor: Dr. Brown
1. Imagine the following game of chance. There are four dollar bills on the table. You roll a
fair die repeatedly. Every time you fail to get a six, one dollar bill is removed. When you
get your f
1.3. Equally likely outcomes
!
Week$2$
If the sample space has finitely many elements and each
outcome is equally likely then for any event A we have
(1.5)
#A
P(A) =
#
Where #A represents the number of favorable outcomes, and #
the total number of outcome
MATH 331 sec002 Fall 2016 Quiz 3
Instructor: Dr. Brown
1. I have a key ring with 7 similar looking keys on it. When I want to open my door I randomly
pick a key and try if it works. If it doesnt work then I pick a key again randomly (it might
even be the
MATH 331 sec002 Fall 2016 Quiz 2
Instructor: Dr. Brown
1. A tourist wants to visit 5 of Americas 12 largest cities. In how many ways can she do this
if
(i) The order of her visits is important.
Solution:
P512 =
12!
= 12 11 10 9 8
(12 5)!
(ii) The order
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
Th
https:/www.coursehero.com/file/7846366/2012exam1sol/
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
Th
https:/www.coursehero.com/file/7846366/2012exam1sol/
sh is
ar stu
ed
* We aren't endorsed by this school
