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.
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
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, 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
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
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
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
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
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
April 23, 2012
Stat 400 EXAM 2
(4.3 5.4)
[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, 2013 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
Counting Techniques.
1. A box contains 5 blue balls numbered from 1 to 5 and 3 green balls
numbered from 1 to 3. How many ways are there to select one blue and
one green ball from this box?
Solution. Consider the following table where the rows show which
STAT400. Sample questions for midterm 2.
1. In this problem you may neglect the probability of twins.
(a) A family has 5 children. Find the probability that they have 2 boys and 3 girls.
(b) A family decides to have children until they have 3 girls. Find
Discrete distributions.
1. A die is rolled 5 times. Let X be the number of times 6 appears. Find P (X = 2),
P (X = 4).
2. A coin is tossed 10 times. Find the probability of 6 heads.
3. 40 % of all customers of Fried Crocodile Restaurant order crocodile st
Conditional Probability.
1. You are given 5 random cards from the standard 52 card deck. You see that the first 4
cards are hearts. What is the probability that you will have flash (that is all 5 cards will be
hearts).
Solution. (Solution I) If you have 4
Conditional Probability.
1. You are given 5 random cards from the standard 52 card deck. You see that the first 4
cards are hearts. What is the probability that you will have flash (that is all 5 cards will be
hearts).
2. A university football team plays
1. Let A, B and C are three events such that P(A) = 0.45, P(B) = 0.30, P(C) = 0.35,
P (A B) = 0.60, P (A C) = 0.60, P (B C) = 0.50, P (A B C) = 0.70.
(a) Compute P (A B), P (A C), P (B C).
(b) Compute P (A B C).
(c) Compute the probability that exactly on
STAT400 Final.
1. Good memory company wants to send advetisements to senior citizens of Happy Town. They send their booklets to all customers of
SuperSlim company. They base their strategy in the following data.
It is known that 25% of adults in that town
Counting Techniques.
1. A box contains 5 blue balls numbered from 1 to 5 and 3 green balls
numbered from 1 to 3. How many ways are there to select one blue and
one green ball from this box?
2. How many outcomes are possible if a die is rolled
(a) 2 times
Independence.
1. A dice is rolled twice. Let
A =cfw_the first number is odd,
B =cfw_the first number is even,
C =cfw_the second number is odd,
D =cfw_the second number is even,
E =cfw_the first number is equal to the second number.
Which of these events a
STAT400 Midterm 2.
1. An urn contains 4 red and 4 blue balls.
(a) If 5 balls are chosen randomly without replacement find the probability that 3 balls will be red and 2 blue.
(b) If 5 balls are chosen randomly with replacement find the probability that 3
Discrete distributions.
1. A die is rolled 5 times. Let X be the number of times 6 appears. Find P (X = 2),
P (X = 4).
Solution. X Bin(5, 61 ). Thus
2 52
1
5
5
P (X = 2) =
0.16,
2
6
6
P (X = 4) =
5
4
4 54
1
5
0.0032.
6
6
2. A coin is tossed 10 times.
HW 5 Problem 3 (6.3 and 6.4 Moler)
Contents
6.3 Moler
6.4 Moler
6.3 Moler
format long
for n=2:30
syms x
a=-1;
b=1;
i=[1:n-2];
% given h=(b-a)/(n-1)
h=2/(n-1);
f(x)=2/(1+x^2);
x=a+i*h;
S=sum(f(x);
T=(h/2)*f(a)+h*S+(h/2)*f(b)
end
%here we see that as n incr
March 9, 2012 Stat 400 EXAM 1
(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 (your text or one 8.5x11
May 16, 2012
ANSWER KEY
Stat 400 FINAL EXAM [Pilachowski]
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. (12 p
May 16, 2012
Stat 400 FINAL EXAM [Pilachowski]
Follow directions carefully:
Number the pages in your answer booklet 1 through 8 (front & back counts as one page) Use exactly ONE answer
page per question.
(2 points) Put your name and other administrative
Stat 400
MIDTERM 2A
1. Suppose X and Y are random variables dened on the same sample space
with the following joint probability mass function.
X\Y
0
1
0
1/4
1/4
1
1/4
0
2
1/8
1/8
(a) Compute the probability mass functions of the random variables X and Y .
Stat 400
MIDTERM 2B
1. Suppose X and Y are random variables dened on the same
sample space with the following joint probability mass function.
X\Y
0
1
0
1/4
1/4
1
2
1/4 1/8
0
1/8
(a) Compute the probability mass functions of the random variables X and Y .
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: schimiak@umd.edu
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
STAT 400 Applied Probability and Statistics I
Fall 2016
Instructor: Lecturer Susan C. Mazzullo
Email: schimiak@umd.edu
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