Math 2314
Chapter 14
Linear Regression Method used to examine the relationship between quantitative
variables and for making predictions.
Sec. 14.1 Linear Equations with One Independent Variable
General Form of a linear equation in one independent variabl
Math 2314
Test 3 Review
(Ch 8 10)
1. A random sample of 50 people was asked to keep a record of the amount of time spent
watching television in a specified week. If the sample mean was 24.4 hours and the
sample standard deviation was 7.4 hours, give a 95%
Math 2314- Test 1 Review (covering Chapters 1-4)
1. Consider the data set below and find:
123, 127, 106, 148, 135, 106, 135, 125, 123, 110, 118, 182, 114, 171, 106, 115, 156
a. Mean
b. Median
c. Mode
d. sample standard deviation
e. range f. Quartiles g. i
Math 2314
Test 4 Review
Ch. 12.1-12.3, 14 & 16
1. An airline is interested in determining the proportion of its customers who are flying
for reasons of business. If the airline wants to be 90% confident that its estimate will be
correct to within 2 percen
ECON 321 Summer 2017
Introduction to International Economics
Online Course
Instructor: Dr. Chris Harris
Email: [email protected]
Office Hours: By appointment
Text: International Economics: Heterodox Approach. Hendrik van den Berg, 2nd edition, M.E.
Sh
Chapter 3. Random Variables (R.V.) and
Probability Distributions
Ch 3.1, 3.2, 3.3, 3.4
1. Definition of a R.V.
2. Discrete and Continuous R.V.s
3. Probability Distribution Functions
4. Cumulative Distribution Function
5. Joint Probability Distributions
6.
Example
It
is claimed that the average ACT score of a high school
student in city of Lincoln is 30 with a standard deviation of
4. To check the claim, an investigator sampled at random
150 high school students in city of Lincoln and computed
the average
Chapter 7
Some Discrete Random Variables and
Applications
In this chapter we will study properties of some commonly used distributions of random variables of discrete type. Besides being familiar with the
properties one should develop the facility to iden
Chapter 8
Some Continuous Random Variables and
Applications
We will now study distributions of some important continuous random variables.
8.1: The uniform distribution:
interval.
This PDF is a constant over a finite
1
, if a < x < b and 0 otherwise.
ba
i
Solutions to Chapter 7 Problems
1. The distribution is binomial. If N is the number that will file claims,
then
!
5
P r(N = n) =
(0.05)n (0.95)5n
n
Hence
P r(N = 0) = (0.95)5 = 0.7738
P r(N = 1) = (5)(0.05)(0.95)4 = 0.2036, and
P r(N 2) = 1 0.7738 0.2036
7.1 The Bernoulli distribution
The Bernoulli distribution is one of the most basic distributions. It
corresponds to a trial, such as a toss of a coin where there are only
two outcomes, say success" and failure."
We can denote by a random variable that ass
Chapter 7 - Discrete Random Variables
148
Problems
1. The probability that a policyholder will file a claim during a year is 0.05.
Amongst a group of 5 independent policy holders find the probability
that at least two will file a claim during a year. (0.0
Chapter 5
Multivariate Distributions
5.1. Joint distribution of discrete variables: There are situations where
one might be interested in more than one random variable. For example, an
automobile insurance policy may cover collision and liability. The los
Chapter 6
Moments of Several Random Variables
6.1. Expected Value : If u(X, Y ) is a function of continuous random
variables X and Y with joint PDF f (x, y), we define the expected value of
u(X, Y ) as
Z
Z
u(x, y)f (x, y) dy dx
E[u(X, Y )] =
(1)
In the di
Solutions to Chapter 6 Problems
1. By Eq.(17), V ar(X1 + X2 + + X20 ) = (20)(2) = 40 and by Eq.(11)
of Chapter 4, V ar(20X1 ) = 400V ar(X1 ) = 800.
2. XY = 1 if and only if X = 1 and Y = 1. Otherwise it is 0. Therefore
E(XY )
E(X)
V ar(X)
E(Y )
V ar(Y )
C
Chapter 6 - Moments of Several Random Variables
130
Problems
1. Let X1 , X2 , X20 be independent identically distributed random variables each with mean 1 and variance 2. Calculate V ar(X1 + X2 + +
X20 ) and V ar(20X1 ). (40, 800)
2. The joint PF of X and
Chapter 5 - Multivariate Distributions
113
Problems
1. You are given the following joint probability function for the random
variables X and Y .
p(0, 0) = 0.18, p(0, 1) = 0.42, p(1, 0) = 0.12, p(1, 1) = 0.28.
(a) Find the marginal PFs of X and Y
(b) Deter
6.1. Expected Value:
Example 6.1.2: Consider the joint probability function p(x, y) of
the random variables X and Y. Find E(X).
1
1
= , = 0.4
=0 =0
6.2. Conditional Expectation:
Problem 10*
A diagnostic test for the presence of a disease has two possible
Chapter 8: Some Continuous Random Variables
and Applications
8.1: The uniform distribution:
=
< <
The stock prices of two companies at the end of any given
year are modeled with random variables and that follow
a distribution with joint density functio
CHAPTER 1
1.
value:
2.50 points
Exercise 1-1
It came as a big surprise when Apples touch screen iPhone 4, considered by many to be the best
smartphone ever, was found to have a problem (The New York Times, June 24, 2010). Users
complained of weak receptio
CHAPTER 5
1.
value:
0.83 points
Exercise 5-1
Consider the following discrete probability distribution.
x
P(X = x)
15
0.14
22
0.40
34
0.26
40
0.20
a. Is this a valid probability distribution?
Yes
No
c. What is the probability that the random variable X is
1.
value:
0.83 points
Exercise 5-1
Consider the following discrete probability distribution.
x
P(X = x)
15
0.14
22
0.40
34
0.26
40
0.20
a. Is this a valid probability distribution?
Yes
No
c. What is the probability that the random variable X is less than
[ii] Homogeneous difierential equation Adi'erentiai equation E- e H I la said to he
dx gist. y
homogeneous, if fix, JP] and 911:. y] are homegenemm intention: of same degree it it
a: [3 Exit
nothewrmen as; = JEEP] = with =Firi'x will
To check that g
$=5x+ has order 1 and is 1st degree
dgr dr _ -
W aw Dhae erder2 endle1etdegree
3
%=Txe3 has order 3 and is 1st degree
d2 T 0 2|]
[J] - [di] +9: [I has order 2 and is Fth degree
1)
2)
3)
4)
5)
Yes; no; no; no
5/6; 1/5
Yes because [conditions of continuity]; no because [conditions of differentiability]
Results may vary.
153.664
6)
cos ( x ) ( x 3 +5 x3 )sin ( x )(3 x2 +5)
3
2
( x +5 x3)
7)
y=
2 x 14
+
3
3
8) 2
y=x 3 is a good exam
Math 2124 Practice Final Exam
The actual test will be a 3 hour exam with only 18 questions, each of which will be worth 2 points. You
will be able to cross out one question with a big X and have it not be graded. Hence you will be graded
on 17 questions,