STAT/MA 41600
In-Class Problem Set #12: September 22, 2014
1. At a certain college, 40% of the students live in a residence hall (on-campus), and the
other 60% of the students live off-campus. Suppose
STAT/MA 41600
In-Class Problem Set #2: August 28, 2015
1. Consider a collection of 9 bears. There is a family of red bears consisting of one father
bear, one mother bear, and one baby bear. There is a
STAT/MA 41600
In-Class Problem Set #7: September 9, 2015
1. Roll three (6-sided) dice. Let X denote the maximum of the values that appear.
1a. Find P (X = 1).
1b. Find P (X = 2).
1c. Find P (X = 3).
1
STAT/MA 41600
In-Class Problem Set #9: September 14, 2015
1. Let Alice roll a 6-sided die and let X denote the result of her roll. Let Bob roll a pair of
4-sided dice and let Y denote the sum of the t
STAT/MA 41600
In-Class Problem Set #4: September 2, 2015
1a. Consider two six sided dice. One die has 2 red, 2 green, and 2 blue sides. The other die
has 3 red sides and 3 blue sides. One die is selec
l. Justify if each of the following statements is true or false. If the statement is false, write a
careful justication or give a counterexample.
(a) (4 points) Given three independent discrete random
Springer Texts in Statistics
Series Editors:
G. Casella
S. Fienberg
I. Olkin
For other titles published in this series, go to
http:/www.springer.com/series/417
Anirban DasGupta
Fundamentals of Probabi
Solutions
Solutions Section I-I
1. There are 6 favorable outcomes, (3,4), (4,3), (6,1), (1,6), (5,2), (2,5),
so prob is 6/36.
2. 8/36
3. There are 6 outcomes where the two dice are equal. Of the remai
CHAPTER
4
Continuous Random
Variables
SECTION 41
DENSITY FUNCTIONS
Remember that a random variable is the numerical outcome of an experiment.
So far (except for the uniform continuous case in Section
2
CHAPTER
Independent Trials and
2-Stage Experiments
SECTION 21
CONDITIONAL PROBABILITY AND
INDEPENDENT EVENTS
The aim of the chapter is to look at experiments with 2 (or more) stages. There
are two t
CHAPTER
5
Jointly Distributed Random
Variables
SECTION 51
JOINT DENSITIES
Before we start on the 2-dimensional continuous case (two random variables
with a joint density function), we'll summarize the
STAT/MA 41600
In-Class Problem Set #1: August 26, 2015
1. Consider a collection of 9 bears. There is a family of red bears consisting of one father
bear, one mother bear, and one baby bear. There is a
STAT/MA 41600
In-Class Problem Set #8: September 11, 2015
1. Suppose that 60% of people in Chicago are fans of da Bears. Assume that the fans
preferences are independent. We interview 3 fans, and we l
STAT/MA 41600
In-Class Problem Set #5: September 4, 2015
1. According to cars.com, the percentages of cars sold are given in the second row of the
following table, and a risk score for each color is g
STAT/MA 41600
In-Class Problem Set #16: September 26, 2014
1. Matilda rolls a die until the first occurrence of 1, and then she stops. Let X denote the
number of rolls until (and including) that first
STAT/MA 41600
In-Class Problem Set #17: September 29, 2014
1. Matilda rolls a die until the eighth occurrence of 1, and then she stops. Let X denote
the number of rolls until (and including) that eigh
STAT/MA 41600
In-Class Problem Set #20/#22: October 6, 2014
(there is no Problem Set #21)
1. A standard deck of 52 cards is shuffled. A person draws them until the first 10 appears,
and then stops. Le
STAT/MA 41600
In-Class Problem Set #18: October 1, 2014
1. Catherine watches raindrops hit the window. The number of raindrops that fall in a fixed
period of time is Poisson with an average of 6 per m
STAT/MA 41600
In-Class Problem Set #19: October 3, 2014
1. A professor estimates that, among 15 students in a seminar, 5 of them enjoyed the seminar
that day, and the other 10 did not enjoy it. He int
STAT/MA 41600
In-Class Problem Set #11: September 19, 2014
Solve all problems by decomposing the random variable in each problem as
a sum of indicator random variables. In other words, find indicator
STAT/MA 41600
In-Class Problem Set #14/#15: September 24, 2014
(there is no Problem Set #13)
1. At a certain college, 40% of the students live in a residence hall (on-campus), and the
other 60% of the
STAT/MA 41600
More Practice Problems: October 6, 2014
1. Rock Block. On a certain radio station, 70% of the songs are rock songs, and 30% of
the songs are pop songs. The songs are selected independent
STAT/MA 41600
Practice Problems: November 5, 2014
1. Let X1 , X2 , X3 be independent exponential waiting times, each with an average of 30
minutes. Let Y = X1 + X2 + X3 .
a. What is the average (in mi
STAT/MA 41600
In-Class Problem Set #3: August 31, 2015
1. It is estimated that, of the people viewing a certain movie over the weekend, 45 percent
were adult women, 42 percent were adult men, and 13 p
CHAPTER
7
Expectation Again
SECTION 71
EXPECTATION OF A RANDOM VARIABLE
Definition of Expected Value
Remember that if X is discrete, then the expectation E(X), also denoted EX,
is given by
E(X) = LXP(
CHAPTER
9
Limit Theorems
SECTION 91
THE CENTRAL LIMIT THEOREM
Sums of random variables turn up a lot. We already know something about
sums of independent binomials, Poissons, exponentials, and normals
CHAPTER
6
Jointly Distributed Random
Variables Continued
SECTION 61
SUMS OF INDEPENDENT RANDOM
VARIABLES
In Section 5.3 you saw how to find the distribution function of any combination
of X and Y (e.g
CHAPTER
8
Conditional Probability
SECTION 8-1
CONDITIONAL DENSITIES
The Conditional Densities fXIY and f ylX
The old rule
P(AIB)
(1)
=
P(A and B)
P(B)
still applies in the continuous case and can be u
CHAPTER
3
Expectation
SECTION 31
EXPECTED VALUE OF A RANDOM
VARIABLE
You already know a lot about finding averages. If your grades for the year are
85% in a 3-point course
90% in a 4-point course
70%
Instructor: Uli Walther
Office: 746 MATH
Phone: 49-41959
E-mail: [email protected]
Purdue University
MA416 Probability
Fall 2016
Syllabus
1
1.1
General Information
Class time / location:
TTh 10: