Math 394
Midterm II Solutions
Winter 2015
Problem 1. Roll two dice. Let A be the event that the sum of dots is a prime
number. Let B be the event that the number of dots on the rst die is 2 or 6. Are events
A and B independent?
Your answer must be justied
Math 394 A
Sample Midterm II Solutions
Winter 2015
Problem 1. Jane put 2 white balls and 3 black balls into an urn. Then she tossed
two coins. She added the same number of white balls to the urn as the number of heads
that showed up on the coins. Peter en
STAT/MATH 394B
Winter 2015
Final Exam
1. Richard and nine of his friends are going in two cars to a friends cabin. Thomas will
be driving one car, and Eileen the other. For reasons of his own, Richard really would
like to go in the same car as Margaret. A
Math 394 A
Sample Midterm I Solutions
Winter 2015
Problem 1. How many ways are there to divide a class of 45 students into four
groups so that the dierence between sizes of any two groups is at most two? Simplify
your answer but there is no need to evalua
Math 394
Sample Midterm I
Winter 2015
Problem 1. How many ways are there to divide a class of 45 students into four
groups so that the dierence between sizes of any two groups is at most two? Simplify
your answer but there is no need to evaluate factorial
Math 394
Final Exam Solutions
Winter 2015
Problem 1. If you order latte at a coee outlet, you have the following choices. You
can choose a size: tall, grande or venti. The choices for the milk are full, 2%, non-fat, or
soy. The strength can be either sing
Math 394
Sample Final Exam
Winter 2015
Problem 1. A group of six couples are going to a restaurant and will sit at a round
table with 12 settings. Every person will choose a seat at the table randomly. What is
the probability that every couple will sit ne
Math 394
Sample Final Exam Solutions
Winter 2015
Problem 1. A group of six couples are going to a restaurant and will sit at a round
table with 12 settings. Every person will choose a seat at the table randomly. What is
the probability that every couple w
HW 1 Solutions
Stat/Math 394, Section A, Summer 2014
(copied from textbooks solution guide and my own comments)
Alternative version of part (a)
First equation:
(
)
[
And then we apply De Morgans laws twice:
(
)]
[(
)
(
)]
(
)
(
)
(
)
(
)
Second equation:
Stat/Math 394, Section A, Summer 2014
A calculus-based, somewhat proof-oriented introduction to probability, leading into more advanced topics
like convergence and limit theorems in Stat/Math 395.
Where: Mechanical Engineering (MEB) 238.
When: 8:30 AM to
HW 1
Stat/Math 394, Section A, Summer 2014
Due: Monday June 30.
In class or to the online dropbox, by mid-class break (9:30).
Well discuss the homework at that time.
Texbook problems are from Chapter 1 (page. 53)
Last years homework 1: #2, 6, 7, 8, 10, 15
HW 2 Solutions
(my comments, interspersed with book solution guide)
Chapter 1:
8 this should now be easy
50 the Birthday problem; its famous and sometimes called a paradox
52 there are 4 kings out of 52 cards; this is about carefully defining the event
56
Stat/Math 394A, Summer 2014, Intro to Probability, Final Exam
Total of 120 points in 4 parts; 30 points per part. Pace yourself at about a point per minute.
Formula sheet
Discrete Distributions
Name
PMF
Mean
Variance
(
)
(
cfw_
Bernoulli
)
Discrete Unifor
HW3
See Tab 'Problem 1' for big calculation problem
Problem 2:
Wikipedia says:
http:/en.wikipedia.org/wiki/Poisson_distribution
a) Prove that the sum of two Poisson RV's is also Poisson
b) Prove:
Problem set 3:
http:/www.athenasc.com/CH3-prob-supp.pdf
Pro
14 Chapter 1 Combinatorial Analysis
Example
6c
How many terms are there in the multinomial expansion of (x1 + x2 + - — ~ + x,)"?
Solution
n
(161 +962 + +Xr)n=Z(n1. nr)x;'1-x;"
where the sum is over all nonnegative integer-valued (n1, . . . , n,) such that