STAT346, section 002 Homework 1 solutions
1. Tenants in a large apartment complex are allowed to own dogs, cats, and rabbits, but
are not allowed to own more than two pets. Write down the sample space
STAT346, section 002 Homework 3 solutions
2-17-15 correction to 4b. The previous answer was correct, but the notation was not. Ive also
added a bit of explanation to the answer.
1. A box contains four
Midterm Exam 1
STAT 346, Spring 2011
Instructions: You cannot use any books or notes. You can use a calculator, but not a computer. You are
not allowed to communicate with anyone (verbally, in writing
Homework 2 solutions
1. The area of the United States composed of the six states Maine, Massachusetts, New Hampshire, Vermont, Rhode Island, and Connecticut is called New England. If for a randomly
se
1. Consider a series of contests between two teams (A and B) with the winner of the series the first team to win three games. The results can be described by the following tree diagram. The letters de
CHAPTER 8
BIVARIATE DISTRIBUTIONS
What we studied so far involved function of one variable
chapter we will deal with functions of two variables
x , the univariate case. In this
x , y , the bivariate c
Chapter 7
Special Continuous Distributions
In this chapter we will study some continuous random variables that frequently appear in the
theory and applications of probability: the uniform random varia
CHAPTER 3
CONDITIONAL PROBABILITY AND INDEPENDENCE
Suppose instead of asking the question What is the probability of an event
question What is the probability of an event
A
called the conditional prob
CHAPTER 5
Special Discrete Distributions
In this chapter we will study some special discrete random variables and their distributions, namely the
Bernoulli random variable, the binomial random variabl
Here is a brief review of one variable calculus.
We will have a brief review of multivariable
calculus later.
Calculus was invented, independently, by Newton and Leibniz. Newton was the first to notic
CHAPTER 1
AXIOMS OF PROBABILITY
Brief History
Probability theory emerged in fifteenth century through the efforts of Italian mathematicians Luca
Paggioli, Noccolo Tartaglia, and Girolamo Cardano. But
HOMEWORK SET I
SOLUTIONS
1. An experiment consists of selecting a point from within the unit circle. Describe the sample
space.
2
2
S=cfw_( x , y)x + y 1
2. Two dice are rolled.
E is the event sum on
Set Theory - A Brief Review
A set is any well-defined collection of distinct objects. We use capital letters to denote sets.
Members of a set are called elements of the set. All elements are drawn fro
CHAPTER 2
COMBINATORIAL METHODS
We will talk about
1.
2.
3.
4.
The General Counting Principle
Factorials
Permutations
Combinations
The General Counting Principle
Suppose a set
E contains n elements an
CHAPTER 4
Distribution Functions and Discrete Random Variables
In many instances we deal with quantities that do not have fixed values, i.e., quantities that
depend on random actions: amount of rain i
Chapter 6
Continuous Random Variables
Let us start by a definition.
X
Definition. Let
be a random variable. Suppose there exists a non-negative, real-valued function
f : R such that for any subset A
o
STAT 346
Assignment 3
Spring 2017
1. Suppose we have a function of the form
cfw_( )
2 x
c
f ( x )= 7 for x=0, 1,2, 3,
0 elsewhere
c >0
where
is a real constant. Determine the value of
c
so that
f
is
Homework 2
1. From a panel of 20 men and 25 women, in how many ways can we obtain a jury of six men and
six women?
N
2. Suppose we have a population of
and we want to select a random sample of size
wi
STAT346, fall 2015, Quiz 5 solutions
1. For each joint distribution function below, indicate if X and Y are independent or not independent, and show and/or explain how you know.
(a) f (x, y) = xex(y+1
STAT346, fall 2015, Quiz 4 Solutions
1. Let X be a discrete random variable with distribution function
t<2
0
1
13 2 t < 4
4 4t<6
F (t) =
13
9
13 6 t < 8
1
t 8.
(a) What is the support?
cfw_2, 4, 6,
STAT346, fall 2015, Quiz 2 solutions
1. Let A and B be events. You may use either logic or set theory notation to answer either (a)
or (b).
(a) Write P(A or B) as a function of P(B) and P(A and B c ).
STAT 346
Probability for Engineers
Fall 2017
George Mason University
Instructor: Martin Slawski
Teaching Assistant: Xiaochen Zhu
Homework 1
due: Wednesday, September 6th, 2017 in class. Maximum possib
STAT 346
Probability for Engineers
Fall 2017
George Mason University
Instructor: Martin Slawski
Teaching Assistant: Xiaochen Zhu
Homework 2
due: Wednesday, September 13th, 2017 in class. Maximum possi
STAT346, section 002 Homework 5 solutions
This question is from A First Course in Probability, Ross, and is posted on blackboard.
However, I use dierent (and better) notation.
A plane is missing, and
STAT346, section 002 Homework 4 solutions
1. I have underlined the key words that indicate you are being given a conditional probability.
Suppose that 50% of the population are male, 5% of the men are
STAT346, section 002 Homework 6 (There are 6 questions, which start on page 3.)
Due at the beginning of class on March 26, 2015
There are probably typos in this. Please let me know if you nd any.
Any
STAT346, section 002 Homework 7 solutions
1. Let X be a discrete random variable with support cfw_0, 4, 9, P(X = 0) = 1/6, and
P(X = 4) = 1/2.
(This is similar, but not identical to the question we di
STAT346, section 002 Homework 9 solutions
The density function for the Gamma distribution is
f (x) =
1
x1 ex/ for 0 x < ,
(a)
, > 0,
(1)
() is called the Gamma function. It is dened for all real numb
STAT346, section 002 Homework 11 solutions
Theorem 1
Let Y1 , Y2 , . . . , Yk be independent random variables, where for i = 1, . . . , k, Yi Binomial(ni , p).
Dene
k
W =
Yi .
i=1
Then W Binomial(n1 +
STAT346, section 002 Homework 10 solutions
When it exists, the moment generating function for a variable X is dened as
Mx (t) = E etX = E [exp(tX)] .
Moment generating function is commonly abbreviated