SAMPLE PROBLEMS FOR FINAL EXAM
MATH 627 Probability, 12/13
1. Find the probability that a hand of ve cards from a deck of 52 cards
contains exactly two distinct pairs and three hearts.
2. Let X and Y
SAMPLE PROBLEMS FOR EXAM I
MATH 627 Probability, 9/13
1. Find the probability that a hand of seven cards contains exactly two
distinct pairs.
2. A fair die is rolled three times. Let X be the smallest
Probability
1.1
1.2
1.3
1.4
1.5
1.6
1. 1
p
BASIC CONCEPTS
PROPERTIES OF PROBABILITY
METHODS OF ENUMERATION
CONDITIONAL PROBABILITY
INDEPENDENT EVENTS
BAYES'S THEOREM
BASIC CONCEPTS
It is usually diffi
Math 3070/6070: Introduction to Probability Practice Problems
Here are some practice problems. These are not comprehensive, meaning they do not
test for everything that I may test for. Nonetheless, th
Geomorphology Problem Set. Due Mon. Dec. 4, 2017
For this homework, first install TopoToolBox:
https:/github.com/wschwanghart/topotoolbox/releases/tag/2.2
Then download a few more things from this dro
Due: November 2, 2017
Math 3070/6070: Introduction to Probability
Problem 1: [ASV 6.26]
Consider two urns, urn A and urn B. In urn A, there are 3 balls numbered 0, 1, 2. In urn
B there are 6 balls num
Math 3070/6070: Introduction to Probability
Due: December 8, 2017
Problem 1: [ASV 9.5]
Suppose that X is a non-negative random variable with E[ X ] = 10.
(a) Give an upper bound on the probability tha
Math 3070/6070: Introduction to Probability Practice Problems
Here are some practice problems. These are not comprehensive, meaning they do not
test for everything that I may test for. Nonetheless, th
Math 3070/6070: Introduction to Probability
Due: November 30, 2017
Problem 1:
Show that Var( X + Y )= Var( X ) + Var(Y ) + 2Cov( X, Y ).
Problem 2: [ASV 8.8]
Our faucet is broken and a plumber has bee
Math 3070/6070: Introduction to Probability
Due: October 18, 2017
Problem 1: [ASV 3.46]
A stick of length ` is broken at a uniformly chosen random location. We denote the length
of the smaller piece b
Due: September 22, 2017
Math 3070/6070: Introduction to Probability
Math 3070 students: do problems 1-4 and problem 5 for extra credit on this assignment. Math 6070 students: do problems 1-5.
Problem
Due: September 29, 2017
Math 3070/6070: Introduction to Probability
Math 6070: There is an extra part to problem 3 for you to do.
Problem 1: [ASV 3.5]
Suppose that the discrete random variable X has a
Math 3070/6070: Introduction to Probability
Due: October 18, 2017
Problem 1: from quiz
Z is a random variable with Z Unif[ a, b], with b > a > 1. Y is another random variable
defined as Y = Z2 .
(a) F
SAMPLE PROBLEMS FOR EXAM II
MATH 627 Probability, 11/13
1. Let X and Y be random variables with the joint probability density
function
fXY (x, y ) =
6 2 xy
(x + )
7
2
0
0 < x < 1, 0 < y < 2
otherwise
SAMPLE Problem Solutions
MATH 627 Probability, 12/13
Beware of the answers given below.
1. Let C (n, r) =
(13,
n!
. CC (522)99 .
r!(nr)!
,5)
2
2. Compute E [Y |X = 6.3] and Y |X and use these values f