STAT 270: Introduction to Probability and
Statistics
Answers to Selected Questions from Textbook Chapter 5
Instructor: Dr. Tim Swartz
By Kasra Youse
October 20, 2012
October 20 2012
5.01:
(a) To evalu
STAT 270: Introduction to Probability and
Statistics
Answers to Selected Questions from Textbook Chapter 4
Instructor: Dr. Tim Swartz
By Kasra Youse
October 20, 2012
October 20 2012
4.04: We have that
STAT 270: Introduction to Probability and
Statistics
Assignment 2: Solutions
Question 1 (a): Dene the event of defect in brakes as B and defect in fuelling
as F. We are now interested in the following
NEED UNITS! NEED RANGE!
READ INSTRUCTIONS! CHECK CALCULATIONS!
Key Concepts:

When we reject H 0 , the results are statistically significant Pairing leads to more sensitive tests when d varies little
Statistics 270 Midterm Exam #2
Name:
Student Number:
1. (4 marks) Let X be a random variable with pmf p(x) = (1/2)x3 for x = 4, 5, 6, . . .
(a) (2 marks) Verify that the pmf values sum to one. Show yo
CHAPTER 3
Section 3.1
1. S: X: FFF 0 SFF 1 FSF 1 FFS 1 FSS 2 SFS 2 SSF 2 SSS 3
2.
X = 1 if a randomly selected book is nonfiction and X = 0 otherwise X = 1 if a randomly selected executive is a femal
Statistics 270 Overview: Study sections 1.1 & 1.2 and do the odd problems. We are interested in drawing conclusions about the characteristics of a population from those of a well chosen subset of the
STAT 270: Introduction to Probability and
Statistics
Supplementary Questions: Set 1
Instructor: Dr. Tim Swartz
By Kasra Youse
September 24 2012
This set includes questions relating to chapter 3 of the
LESSON 23
(corresponds to section 5.6 of the textbook)
The Central Limit Theorem (CLT)
One of the most important theorems in statistics!
Original version of CLT says:
When independent and identically
LESSON 6
[corresponds to Sections 3.1 and 3.2 of the textbook]
The definition of probability starts with the concept of random experiments. The
textbook calls it experiments in a broad setting. These
LESSON 4
Measures of Dispersion
(See the example on p15 of the textbook)
Important:
Measures of location such as mean and the median, are insufficient to summarize a
dataset
Mean or median will only m
LESSON 12
[Corresponds to section 4.2 of the textbook]
Expectation (= Expected Value)
Definition:
Expected value of a discrete r.v, X, is given by
E(X) = x. pX(x), where the sum is over all x.
Example
LESSON 29
(corresponds to sections 7.1 and 7.2 of the textbook)
Inference based on Two Samples
[Please read pp 145 152]
Using Normal theory:
Assume two independent normal populations:
Population (1):
LESSON 11
[Corresponds to section 4.1 of the textbook]
Random Variables
Simple Definition:
A random variable (r.v) is a function of the sample space.
Notation: Usually Capital letters at the end of th
LESSON 22
Statistics
The word statistics is used in two contexts: one, as the name for the subject, statistics; two,
any function of data in a sample is also called a statistic.
Example 1:
Suppose you
LESSON 25
(corresponds to section 6.1.1 of the textbook)
Interval Estimation using Normal Theory
Let (X1, X2, , Xn) be a random sample (i.i.d) from N(, 2).
Assume that is unknown and that we want to o
LESSON 10
[Corresponds to section 3.6 of the textbook]
Probability Examples (Continued)
Example 1: (Birth Day Problem)
Suppose there are 5 people (I am using 5 instead of 30 to make life easier) in a
LESSON 7
[corresponds to Sections 3.3 and part of 3.4 of the textbook]
Probability Definitions
1. Axiomatic Definition [Due to Kolmogorov, 1933]
2. Symmetry Definition [for a finite number of equally
LESSON 9
[Corresponds to section 3.6 of the textbook]
Probability Examples
Example 1:
Suppose in a class of 40 students 23 are female. Five students are drawn at random
to form a committee. [Note that
LESSON 16
(corresponds to Introduction to Chapter 5 and section 5.1 of the textbook)
Continuous Distributions
In Chapter 4, we discussed discrete r.vs and their distributions (namely, binomial, and
Po
LESSON 19
(corresponds to section 5.3 and 5.3.1 of the textbook)
Solutions to some homework:
5.17
Wage, X ~ N (15.90, (1.50)2)
(a) Need P(13.75 < X < 16.22) as a proportion.
(Here, X is given and you
*LESSON 31*
(corresponds to section 7.4 of the textbook)
Paired Samples
Paired data data of the form (X1, Y1), (X2, Y2), ,(Xn, Yn) , i.e. n pairs of observations.
Note that paired observations within
LESSON 8
[corresponds to part of section 3.4 and section 3.5 of the textbook]
Example 1:[Exercise 3.15 of the textbook]
Automobile manufacturer: Possibility of recalling its 4door sedan. (vehicles wi
LESSON 27
(corresponds to section 6.4 of the textbook)
Hypothesis Testing (Contd.)
[Students must read pp 134139 of the textbook]
Level of Significance ()
Recall the pvalue criterion for rejecting a
LESSON 26
(corresponds to sections 6.1.2, 6.2, and 6.3 of the textbook)
Interval Estimation for a Population Proportion (p)
Will use C.L.T applied to Bernoulli distribution
Example 1:
Suppose we want
LESSON 14
(covers sections 4.3 and 4.4 of the textbook)
Binomial Distribution (Contd.)
The importance of binomial comes from the fact that, random experiments with more than
2 possible outcomes can al
LESSON 24
(corresponds to sections 5.5, 5.6, and 6.1 of the textbook)
Summary of Sections 5.5 and 5.6 [= Lessons 22 and 23]
Section 5.5 (Lesson 22) summary:
X is a (random) statistic.
If X1, X2, , Xn
LESSON 17
(corresponds to sections 5.1 and 5.2 of the textbook)
Expectation of a continuous (cts) r.v
Recall that for discrete r.v: E(X) = x p(x) . Similarly,
For cts case, = E(X) = x f(x) dx and 2 =
FULL NAMES: STUDENT ID:
STAT 270 Midterm 1, Fall 2017
1. (5 marks) Two fair dice are rolled. Given that the sum is 9, What is the probability that the rst
die is 4?
A: SM? 1.5 7 . / 1
3. ,.+ die .5 42
LESSON 3
[Corresponds to sections 2.1, 2.2, and 2.3.1 of the textbook]
Descriptive Statistics: (in detail)
Goal is to summarize data in a convenient form so that features of the data may be
easily rev