STAT 3502 (Winter Term 2013)
Solutions to Assignment 1
1. (a) P (A B C) = P (A)P (B)P (C) = (.7)(.6)(.8) = .336.
(b) P (at least one flight is full) = 1P (no flight is full) = 1P (A0 )P (B 0 )P (C 0 )
= 1 (.3)(.4)(.2) = 1 .024 = .976.
(c) P (A0 B 0 C) = P
9.1
Chapter 9
Inferences Based on Two
Samples
1
9.1
9.2 z Tests and Confidence Intervals for a
Difference Between Two Population Means
In many applications, it is of interest to study the
difference between the means of two populations. In
fact, by studyi
FORMULA SHEET
CHAPTER 2
Law of Total Probability: P( B) PB | A1 P A1 . PB | An P An ;Bayes: P Ai | B
Conditional Probability: P A | B
PB | Ai P Ai
P( B)
P A B
; Union of 2 events: P A B P( A) P( B) P A B ;
P( B)
Union of 3 events: P A B C P( A) P( B)
6.1
Chapter 6
Point Estimation
1
6.1
6.1 Some General Concepts of Point Estimation
A point estimate of a parameter is a single number
that can be regarded as a sensible value for . A point
estimate is obtained by selecting a suitable statistic
and computi
3502 Assignment 1 due Wed. Feb. 6th in class. No late assignment will be
accepted. TAs will NOT accept assignments directly from students.
1. An airliner has 2 p.m., 8 p.m., and 10 a.m. flights from Montreal to Frankfort, Paris, and
Vancouver respectively
Note: all denitions are from your textbook
CHAPTER 1
What is Statistics?
The discipline of statistics teaches us how to make intelligent judgments and informed decision in the presence of uncertainty and variation.
Branches of Statistics
Descriptive Stat
Chapter 1: Overview and Descriptive Statistics
CHAPTER 1
Section 1.1
1.
a.
Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post
b.
Capital One, Campbell Soup, Merrill Lynch, Pulitzer
c.
Bill Jasper, Kay Reinke, Helen Ford, David Menede
3502 Tutorial 3
1. Compute the following binomial directly from the binomial formula:
a. b(3; 8, .35) b. b(5; 8, .6), c. P (3 X 5) when X Bin(7, .6).
2. A company that produces ne crystal knows from experience that 10% of its goblets have
cosmetic aws and
CHAPTER 9
Inference Based on Two Samples
Test and Condence Intervals for a Dierence Between Two Population Means
Case I: Normal populations with known variances
Assumptions:
2
1. X1 , X2 , , Xm is a random sample from a population with mean 1 and variance
CHAPTER 8
Test of Hypotheses Based on a Single Sample
Hypothesis testing is the method that decide which of two contradictory claims about the
parameter is correct. Here the parameters of interest are population mean and proportion.
Hypotheses and Test Pr
CHAPTER 5
Jointly Distributed Random Variable
There are some situations that experiment contains more than one variable and researcher
interested in to study joint behavior of several variables at the same time.
Jointly Probability Mass Function for Two D
CHAPTER 7
Statistical Intervals Based on a Single Sample
The point estimate report a single number that does not provide any information about the
precision and reliability of estimation. An alternative estimate is interval estimate. A condence interval i
STAT 3502
Tutorial # 8
1. Let X1 , X2 , , Xn represent a random sample from a Rayleigh distribution with pdf
f (x; ) =
x x2 /(2)
e
x>0
a. It can be shown that E(X 2 ) = 2. Use this fact to construct an unbiased estimator
of based on
Xi2 .
b. Estimate from
STAT 3502
Tutorial # 9
1. In an experiment designed to measure the time necessary for an inspectors eyes to
become used to the reduced amount of light necessary for penetrant inspection, the
sample average time for n = 9 inspectors was 6.32 sec and the sa
STAT 3502
Tutorial # 6-Summer 2011
1. Suppose the time spend by a randomly selected student who uses a terminal connected
to a local time sharing computer facility has a gamma distribution with mean 20 min
and variance 80 min2 ?
a. What are the values of
Note: all denitions are from your textbook
CHAPTER 1
What is Statistics? The discipline of statistics teaches us how to make intelligent judgments and informed decision in the presence of uncertainty and variation. Branches of Statistics
Descriptive Stat
CHAPTER 3
Random Variable
A rule that associate a number to each outcome of an experiment (or each outcome in S) is
random variable.
Bernoulli random variable: Any random variable whose only possible values are 0 and 1
Example: Give three examples of Bern
CHAPTER 2
PROBABILITY
Probability is used in inference statistics as a tool to make statement for population from
sample information.
Experiment is a process for generating observations
Sample space is all possible outcomes of an experiment.
Event is a
CHAPTER 4
Continuous Random Variables and Probability Distributions
Basic denitions and properties of continuous random variables
Continuous random variable: A random variable is continuous if its set of possible values
is an entire interval of numbers.
P
CHAPTER 6
Point Estimate
The goal in this section, is to estimate a parameter of population based on a random sample
of size n. If we consider a single number as a parameter estimate, named it point estimate.
Therefore, point estimate is a suitable statis
Chapter 8
Tests of
Hypotheses Based
on a Single
Sample
8.1
Hypotheses
and
Test Procedures
Hypotheses
The null hypothesis, denoted H0, is the
claim that is initially assumed to be true.
The alternative hypothesis, denoted by
Ha, is the assertion that is co
Chapter 9
Inferences Based
on
Two Samples
9.1
z Tests and Confidence
Intervals for a
Difference Between
Two Population Means
The Difference Between Two
Population Means
New Notation
Assumptions:
1. X1,Xm is a random sample from a
2
population with m1 and
Chapter 3 -Discrete Random Variables and Probability Distributions
Announcements
Some of the TAs pointed out an alternate approach to Q 3 part
c. I will post that solution on the website.
I posted a clarication to Q5b on the website and sent out an
email.
Ch. 5 Jointly Distributed Random Variables and Random Samples
Ch. 5.1 Jointly Distributed Random Variables
Ch. 5.1 Jointly Distributed Random Variables
The probability mass function (pmf) of a single discrete rv X
species how much probability mass is plac
Additional Question for Tutorial 2 (in place of question 2 which was done in
class)
Show that for any three events A,B and C with P(C) > 0,
P (A B|C) = P (A|C) + P (B|C) P (A B|C)
1
Additional Question for Tutorial 2 (in place of question 2 which was done in
class)
Show that for any three events A,B and C with P(C) > 0,
P (A B|C) = P (A|C) + P (B|C) P (A B|C)
Solution
P (A B|C) =
P [(A B) C]
P (C)
P [(A C) (B C)]
=
P (C)
P [A C] + P
Chapter 2 - Probability
Notes From Last Class
In Q. 54 (d) I accidentally put
P[A1 A2 A3 |A1 A2 A3 ] =
P[ (A1 A2 A3 ) (A1 A2 A3 )]
P[A1 A2 A3 ]
but it should have been the intersection,
P[A1 A2 A3 |A1 A2 A3 ] =
C. Gravel (Carleton)
P[ (A1 A2 A3 ) (A1 A2 A
Additional Points From Last Class
In the deck of cards example, the experimental set up allowed
us to observe N(A) and n, and since they are equiprobable
N(A)
events, we can apply the formula P(A) = n . However, the mail
delivery example, P(A) = 0.6, henc