March 9, 2012
Stat 400 EXAM 1
(2.1 4.2)
[Pilachowski]
SOLUTIONS
Note: While wed like to guarantee that this answer key is 100% correct, there may be typos we missed in the
proofreading. If you think an answer is wrong, check with your instructor or TA.
1.
April 23, 2012 Stat 400 EXAM 2
(2.1 4.2)
[Pilachowski]
Follow directions carefully:
Use exactly ONE answer sheet per question (use the back of the sheet if needed).
Put your name and the question number on EACH page.
You may use one 8.5x11 page and a c
Stat 400, chapter 2, Probability, Conditional Probability and Bayes Theorem Solutions
supplemental handout prepared by Tim Pilachowski
Example 2: The Gallup organization conducted 10 separate surveys conducted from January through May 2009.
At the time of
March 14, 2013 Stat 400 EXAM 1
(2.1 4.2)
[Pilachowski]
Follow directions carefully:
Counting front and back as one page, number the pages in your answer booklet 1 through 8.
Answer question 1 on answer page 1, question 2 on answer page 2, etc.
You may u
Spring 2015
Stat 400 EXAM 2
(4.3 5.4)
[Pilachowski]
Follow directions carefully:
Counting front and back as one page, number the pages in your answer booklet 1 through 8. Answer question 1 on answer
page 1, question 2 on answer page 2, etc. Use page 8 if
Stat 400, chapter 2, Probability, Permutations and Combinations - SOLUTIONS
supplemental handout prepared by Tim Pilachowski
Examples A. through F. have answers on the supplement, with explanations.
Example G. In a game of bridge, using a standard deck of
Stat 400, chapter 2, Probability, Permutations and Combinations
supplemental handout prepared by Tim Pilachowski
An arrangement in which the order of objects or events makes a difference, e.g. RYB RBY, is called a
permutation. When the order of objects or
1) Your statistics instructor claims that 60 percent of the students who take her Elementary
Statistics class go through life feeling more enriched. For some reason that she can't quite
figure out, most people don't believe her. You decide to check this o
Homework 1
1. Section 2.2: 20
2. Section 2.2: 26
3. A club is electing its four officers.
a. Is this an example of a combination, permutation, or both? Explain your answer.
b. If the club has fifty members, how many different ways can slates of officers b
Stat 400, chapter 2, Probability, Conditional Probability and Bayes Theorem
supplemental handout prepared by Tim Pilachowski
Example 1. Silver Springs, Florida, has a snack bar and a gift shop. The management observes 100 visitors, and
counts 65 who eat i
STAT 400-001 Applied Probability &
Statistics I
Lecture 09 Section (2.5): Independence
Independence
Some Examples
Lecture 9 Section 2.5:
Independence
1
Event Independence
Two events are independent if any one of the
following equivalent statements are tr
Stat 5571 Homework 6, Fall 2016
Solution
All exercises below are from chapter 4 on the textbook. Show all the work. I will take
points off if only the final answers are shown.
1. Exercise 3.
(a)
(b)
(c)
(d)
(e)
(f)
52
P (A) = P (get two aces) = 42 48
/ 5
REMEMBER IN STATISTICS SOMETHING IS UNUSUAL IF THE PROBABILITY OF IT OCCURING IS
0.05 OR LESS.
A researcher believes the mean number of seeds for a certain variety of Marigold has decreased
from 125.2 seeds per plant. It is known that the population stand
Stat 5571 Homework 10, Fall 2016
Solution
Chapter 7
1. Consider a random sample of size n from a distribution with CDF F (x) = 1
1 x < , and zero otherwise. Define Yn = min1in Xi .
1
x
if
(a) Derive the CDF of the Yn .
FYn (y) = P (Yn y) = P (min1in Xi y
Stat 5571 Homework 2, Fall 2016
Solution
1. Exercise 31.
(a) The total number of balls is 5 + 3 + 7 = 15. P (both are red) = P (A1 A2 )
where
Ai isthe event that the ith ball is red. P (A1 A2 ) = P (A1 )P (A2 |A1 ) =
7
6
1
= .
15
14
5
(b) We can do the
These are just a few of the types of problems you could see on Test 2. And remember, the tests are
cumulative, so you can see some problems like you saw on Test 1.
According to American Airlines, its Flight 215 from Orlando to Los Angeles is on time 85% o
Binomial with n = 8 and p = 0.62
Binomial with n = 10 and p = 0.62
x
0
1
2
3
4
5
6
7
8
x
0
1
2
3
4
5
6
7
8
9
10
P( X <= x )
0.00043
0.00611
0.03852
0.14427
0.35994
0.64145
0.87111
0.97817
1.00000
P( X <= x )
0.00006
0.00109
0.00861
0.04133
0.13476
0.31769
Please use the standard normal table to answer the following questions that use the Normal
Distribution!
Insect traps are checked periodically, the mean number of insects trapped is 0.75. The
distribution of insect counts is skewed with a standard deviati
Terminals on an on-line computer system are attached to a communication line to the central computer
system. The probability that any terminal polled is ready to transmit is 0.95. Each terminal is
independent of one another. Use this information to answer
Stat 5571 Homework 5, Fall 2016
Solution
1. Exercise 3.
(a) This is a binomial distribution with n
and p = 0.5. The probability of
= 10
8
hitting eight shots is b(8; 10, 0.5) = 10
(0.5)
(1
0.5)108 = 0.0439.
8
(b) If p = 0.6, then b(8; 10, 0.6) = 10
(0.6
Stat 5571 Homework 2, Fall 2016
Solution
1. Exercise 2.
There are 12 sample points in the sample space S, namely,
S = cfw_(1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)
where the first number denotes the val
Stat 5571 Homework 6, Fall 2016
Solution
All exercises below are from chapter 5 on the textbook. Show all the work. I will take
points off if only the final answers are shown.
1. Exercise 2.
Let X1 , X2 , . . . , X144 be the weights of these baseballs. T
Stat 5571 Homework 4, Fall 2016
Solution
Every question is worth 0.5 point.
1. Exercise 23.
The pmf of X is
x
f (x)
1
1/8
2
2/8
5
5/8
P
x xf (x) = (1)(1/8) + (2)(2/8) + (5)(5/8) = 30/8.
P
2
2
2
2
(b) E(X 2 ) =
x x f (x) = (1 )(1/8) + (2 )(2/8) + (5 )(5/8)
Stat 5571 Homework 6 Part 2, Fall 2016
Solution
1. Exercise 19.
R1Ry
R1 2
(a) 0 0 k(x + y)dxdy = k 0 3y2 dy = k/2 which implies k = 2.
R1
Ry
(b) f1 (x) = x 2(x + y)dy = 3x2 + 2x + 1 for 0 x 1. f2 (y) = 0 2(x + y)dx = 3y 2
for 0 y 1.
(c) The joint CDF is F
Stat 5571 Homework 9, Fall 2016
Solution
All exercises below are from chapter 6 on the textbook.
1. Exercise 13.
1
[f ( y) +
2 y X
1/2
y
y
contribute and fY (y) = 21 y ( 24
+ 24
) = y24 .
1/2
term will contribute and fY (y) = y48 .
From Example 6.2.2, fY
1. Given two events C and D in a sample space S, if we know that P(C) =
0.3 and P(D | C) = 0.2,
a. PC D= 0.06
b. Events C and D are not independent
2. Given two events E and F in a sample space S, if we know that P(E) =
, P(F) = 1/3, and P(EF) =
a. P(E|F
STAT 400 Applied Probability and Statistics I
Fall 2016
Instructor: Lecturer Susan C. Mazzullo
Email: [email protected]
Office: MTH 3316
Office Hour: MW: 11:15-11:45AM and 1:15-2:15PM. These office hours are by appointment only that
is, email me to let me
These are just a few of the types of problems you could see on Test 2. And remember, the tests are
cumulative, so you can see some problems like you saw on Test 1.
According to American Airlines, its Flight 215 from Orlando to Los Angeles is on time 85% o
Comparing Three or More Means
Objectives
1. Verify the requirements to perform a oneway ANOVA
2. Test a hypothesis regarding three or more
means using one-way ANOVA
Analysis of Variance
Topic 16
1
Analysis of Variance
Analysis of Variance (ANOVA) is an
in
Topic 15: Deeper Look at Regression
1. Have a better understanding of the SAS
output In Regards to Simple Regression
2. Read and interpret output in SAS for
Simple Regression
3. Have a better understanding of the SAS
output In Regards to Multiple Regressi
Comparing Three or More Means
Objectives
1. Verify the requirements to perform a oneway ANOVA
2. Test a hypothesis regarding three or more
means using one-way ANOVA Using SAS
Analysis of Variance Using SAS
Topic 17
1
Analysis of Variance Using SAS
1.
2.
3
Topic 12: Descriptive Study of Bivariate Data
Characteristics of bivariate populations & sample data
Qualitative (categorical)
Quantitative (measurement)
Cross-tabulations of categorical data
Analysis approaches
Scatter diagrams
Correlation coeffic
Topic 13
Simple Regression
Simple Regression
Topic 13
1
Topic 13: Simple Regression
1. Regression
2. Residuals
Simple Regression
Topic 13
2
Topic 13: Simple Linear Regression
Often we would like to be able to predict a desired variable value
based on a kn