Probability Formulas
1
Basics of Probability Distributions
X Bernoulli(p) when:
X cfw_0, 1
where
Y Binomial(n, p) when:
P r(X = 1) = p
Y = X1 + X2 + . + Xn
Conditional probability:
P r(Y | X) = P r(Y
Y is independent of X if:
given
P r(Y | X) = P r(Y
BADM 275
Decision Analysis
Problems (Solutions)
BADM 275
Decision Analysis
Problems (Solutions)
1. Models that do not involve risk or chance are _.
a)
b)
c)
d)
e)
probabilistic models
postoptimality models
deterministic models
MIS models
none of the above
BADM 275(section)
(last names of all group members)
Case: (name of case)
Semester/Year
Introduction
A one paragraph overview of the case in condensed form. There is no need to rewrite the case
just give a simple introduction in no more than five sentences
BADM 275 Final Exam Review Questions 1
Network Models:
1. Given the following distances between destination nodes, what is the minimum distance that
connects all the nodes?
From
1
1
2
2
3
(a)
(b)
(c)
(d)
(e)
To
2
3
3
4
4
Distance
200
300
350
350
250
100
7
BADM 275 Midterm Review Questions 1
Decision Analysis:
1. Which of the following is true about the expected value of perfect information?
a)
b)
c)
d)
e)
it is the amount you would pay for any sample study
it is calculated as EMV minus EOL
it is calculated
Extra Problems: Probability (Solutions)
1
The Normal Distribution via Excel
Suppose R N (0.1, 0.0016). In Excel, use the =NORM.DIST(., TRUE) function to determine the following:
1. What is P (R < 0)?
Answer: Using =NORM.DIST(0,0.1,0.04,TRUE), we get 0.006
Extra Problems: Regression (Solutions)
1
Simple Linear Regression
For this question, use the beer data (beer.xlsx) discussed in Lecture 2.pdf and on Exam 3.
We want to know how the number of beers a student claims to be able to drink is related to the
stu
Extra Problems: Statistical Inference (Solutions)
1
Confidence Intervals for Voting
It is election night and you are working for a TV news service in Florida. You are covering a race
between two candidates, George and Al. Assume that all voters in the sta
Problems: Probability 1 (Solutions)
1
Understanding How to Read a p.d.f.
Consider the figure below. The plot shows the probability density functions (p.d.f.) of three
continuous random variables: X, Y , and Z. The random variables X and Y have the followi
Problems: Probability 2 (Solutions)
1
The Binomial Distribution
There is going to be an election for a new mayor next week. Suppose you work for a local newspaper,
and your boss has asked you to poll voters to determine what the outcome of the election mi
Extra Problems: Summarizing Univariate and Bivariate Data
(Solutions)
1
Histograms and Time Series Plots
The objective of this page is to get practice with basic Excel graphs. For the following questions, use
the tutorial files How to make a Histogram.pdf
Exam 3 Extra Problems
1
Confidence Intervals for Voting
It is election night and you are working for a TV news service in Florida. You are covering a race
between two candidates, George and Al. Assume that all voters in the state of Florida vote for
one o
Exam 1 Extra Problems Solutions
1
Histograms and Time Series Plots
The objective of this page is to get practice with basic Excel graphs. For the following questions, use
the tutorial files How to make a Histogram.pdf and How to make a Time Series Plot.pd
Summarizing Univariate and Bivariate Data Solutions
1
Understanding Univariate Data
Consider the following data, complete the table and answer questions 1 through 3.
Period (t)
Value (X)
(Xt X)2
1
10
81
2
15
16
3
30
121
4
23
16
5
17
4
1. What is the mean
Probability 1
1
Understanding How to Read a p.d.f.
Consider the figure below. The plot shows the probability density functions (p.d.f.) of three
continuous random variables: X, Y , and Z. The random variables X and Y have the following
normal distribution
Probability 2
1
The Binomial Distribution
There is going to be an election for a new mayor next week. Suppose you work for a local newspaper,
and your boss has asked you to poll voters to determine what the outcome of the election might
be. For the questi
Statistical Inference Formulas
1
Standard Error and Confidence Intervals
Standard error for the sample mean:
95% confidence interval for the sample mean:
SX
CI = X 2
n
SX
SE =
n
Standard error for p:
r
SE =
2
95% confidence interval for p:
r
p (1 p)
Statistical Inference
1
Confidence Intervals and Plug-in Predictive Intervals
There is concern about the speed of automobiles traveling over a particular stretch of highway. For
a random sample of n = 7 automobiles, radar indicated the following speeds me
Probability 2 Solutions
1
The Binomial Distribution
There is going to be an election for a new mayor next week. Suppose you work for a local newspaper,
and your boss has asked you to poll voters to determine what the outcome of the election might
be. For
Probability 1 Solutions
1
Understanding How to Read a p.d.f.
Consider the figure below. The plot shows the probability density functions (p.d.f.) of three
continuous random variables: X, Y , and Z. The random variables X and Y have the following
normal di
Summarizing Univariate and Bivariate Data Formulas
1
Univariate Data
Mean: X =
P
all i
Xi
Variance: VX =
n
Sum of squares: SSX =
2
P
all i (Xi
X)2
P
2
all i (Xi X)
n1
Standard deviation: SX =
qP
2
all i (Xi X)
n1
The Emperical Rule
Approximately 68%
Exam 2 Extra Problems
1
The Normal Distribution via Excel
Suppose R N (0.1, 0.0016). In Excel, use the =NORM.DIST(., TRUE) function to determine the following:
1. What is P r(R < 0)?
2. What is P r(0 < R < 0.1)?
3. What is P r(R > 0.15)?
1
The following p
Exam 1 Extra Problems
1
Histograms and Time Series Plots
The objective of this page is to get practice with basic Excel graphs. For the following questions, use
the tutorial files How to make a Histogram.pdf and How to make a Time Series Plot.pdf
for assi
Exam 2 Extra Problems Solutions
1
The Normal Distribution via Excel
Suppose R N (0.1, 0.0016). In Excel, use the =NORM.DIST(., TRUE) function to determine the following:
1. What is P r(R < 0)?
Answer: Using =NORM.DIST(0,0.1,0.04,TRUE), we get 0.00621.
2.
Summarizing Univariate and Bivariate Data
1
Understanding Univariate Data
Consider the following data, complete the table and answer questions 1 through 3.
Period (t)
Value (X)
1
10
2
15
3
30
4
23
5
17
1. What is the mean of the data set?
2. What is the v
Problems: Summarizing Univariate and Bivariate Data (Solutions)
1
Understanding Analytical Notation
1. Determine the solutions to the following analytical expressions. Can the solution be reduced
to a number?
P3
Answer: 1 + 2 + 3 = 6; Yes
i=1 i
Pn
Answer: