STA 3032
Exam 2 Review
March 22, 2016
CHAPTER 4
Continuous Random Variables
Continuous random variables
possible values comprise either a single interval on the number line
(for some A < B, any number x between A and B is a possible value) or
a union of
STA 3032
Probability and Statistics for
Engineers
Sections 4.3 and 4.4
October 15, 2015
Basma Selim, Ph.D.
1
z Notation for z Critical Values
In statistical inference, we will need the values on the
horizontal z axis that capture certain small tail areas
STA2023H Fall 2012
Chapter 4: Numerical Methods for Describing Data
In Chapter 1 we learned there are two processes in statistics:
Describing sets of data
Drawing conclusions
In Chapter 4 we are going to learn ways to organize and describe data sets.
In
STA2023H Fall 2012
Chapter 3: Graphical Methods for Describing Data
Graphing is a way to organize data to better detect _patterns_ and _trends_. Different types of graphs
are appropriate for different types of _data_
Graph
Pic
Type of data
Dot Plot
Quanti
1) Suppose a bookie will give you $6 for every $1 you risk if you pick the winner in 3 ballgames. For
every $1 bet, you either lose $1 or gain $6. What is the bookies expected earnings per game?
2) Given the following probability distribution,
a)
b)
c)
d)
At a particular apartment complex, there has been an average of 3 break-ins per month. Find the
probability of exactly one break-in during that month. Find the probability that there is at least 2.
You are taking a 7 question exam with each question being
SARC is hiring new tutors for the tutoring positions for statistics, chemistry 1 and biology 1. 12 people
applied for statistics, 23 people applies for chemistry 2 and 15 applied for biology 1. In how many
ways can the boss choose the new tutors? Assume o
On an exam that was bell-curved/normally distributed, the average score was a 70 with a standard
deviation of 9. What percent of the class scored between a 52 and 88? If you scored a 52, what
percent of the class scored below you? What value represents th
Angela is interested in finding the average age of students in the STA 2023 course. In order to
determine this, she takes the age of 65 students of the 435 students and finds the average to be 21.36.
From this information, identify the following:
Populati
The following is a 95% confidence interval for p: (0.34,0.68). How large was the sample used to
construct the interval?
An estimate is needed of the average age of patients in a doctors office within .1 with 95%
confidence. The standard deviation was foun
Angela is interested in finding the average age of students in the STA 2023 course. In order to
determine this, she takes the age of 65 students of the 435 students and finds the average to be 21.36.
From this information, identify the following:
Populati
STA 3032 - Probability and Statistics for Engineers
Spring Semester, 2016
Section 0R03 (combined with all remote sections)
Instructor: Dr. Mohamed Awwad
Email: mohamed.awwad@ucf.edu
Office: ENGR 2, Room 427
Office Hours: Tuesdays 1:30 pm - 4:00 pm and by
STA 3032-CMB - Probability and Statistics for Engineers
Spring 2016 Term Project
Available: February 9th, 2016
Due: April 19th, 2016
Instructions:
i.
Use Excel, Minitab or any other software of your choice to analyze the given data. If you
decide to use E
Tentative Course Schedule: Stat 500 Fall 2015
Getting Started
Complete the activities in the Getting Started folder (see the Lessons tab) by
August 28th
Read Proctor Information Form (Final Only) and start working on this.
Lesson 1 (Monday August 24th t
4.1 - Discrete Probability Distributions
Expected value of X:
Variance of X:
E ( X )= P ( xi )( x i)
2
2
Var ( X )= P(x i )( xi )[ E ( X ) ]
4.2 - Binomial Distributions
A special discrete random variable is the binomial. We have a binomial experiment if
6.1 - Inference for the Binomial Parameter: Population Proportion
RECALL: If np5 and n(1p)5 then
^p is approximately normal with mean and sd:
p ( 1 p )
n
One-sample Z-interval for the population proportion, p.
1.
Assumptions needed to check before one can
It all begins with Y
wi
th
X
y
Lin
e
ar
t
re
nd
Use Y values to
compute b0 and b1
Least squares line
^
y b0
bx
1
y
pr
ed
es
tim
at
es
And continues with
^
i ct
s
Y = 0 + 1x +
^
y Essentially performs two tasks:
Estimates the mean of Y for a specific x
Test1 Review
Learning objectives and Outcomes for lessons 1 to 6 is an excellent guide to
prepare for this test. You may find the following key words/phrases useful .
Parameters, estimates, residuals and their properties, least squares criterion,
best fit
It all begins with Y
wi
th
X
y
Lin
e
ar
t
re
nd
Use Y values to
compute b0 and b1
Least squares line
^
y b0
bx
1
y
pr
ed
es
tim
at
es
And continues with
^
i ct
s
Y = 0 + 1x +
^
y Essentially performs two tasks:
Estimates the mean of Y for a specific x
Lesson 4 Review - Detection of LINE assumptions
violations , outliers and model inadequacy.
Method: Residual Analysis using plots
residual vs fit detects
Non linearity
Unequal variances
Outliers
2. residual vs order detects
Non independence
normal probab
Lesson 5. Multiple Linear Regression(MLR)
- Review
Here we extended the SLR equation to include several
predictor variables.
Matrix form is a convenient way to work with MLR
Y=X +
Recall
how you can write the data values into Y and X respectively.
X is c
Lesson 1
Least Square Criterion says to "minimize the sum of the squared prediction errors.
What does b0 tell us? If x=0 is within the scope of the model, then b0 is the predicted mean
response when x = 0. Otherwise, b0 is not meaningful.
What does b1 te
MAS 3105 suggested problems
For these problems, the exercises at the beginning of the section are a good way to get going
even if they are not assigned. So start in the following lists with problems you know you need to
write out to see if you can do it.
QUIZ DEFINITIONS
Subspace
o If S is a nonempty subset of vector space V, and S satisfies the conditions
x S whenever x S for any scalar
x+ y S whenever x S y S
o Then S is said to be a subspace of V
Null Space
o If A is your matrix, the null-space is th
Descriptive statistics, where we will organize and summarize data utilizes numerical and
graphical methods to look for patterns in a data set, to summarize the information revealed in a
data set and to present that information in a convenient form. 6
Inf
STA2023: Statistical Methods I
(3 Credit Hours) Fall 2014: Section 0004 MWF 2:30PM 3:20PM CB1 104
Instructor: Kelcey Ellis
Email: kelcey@ucf.edu
Phone:
Office:
407-823-6522
TCII 211D
Note: All course correspondence must be sent using the conversations too
STA2023 Fall 2014
Chapter 2: Methods for Describing Sets of Data
In Chapter 1 we learned there are two processes in statistics:
Describing sets of data
Descriptive
Drawing conclusions
Inferential
In Chapter 2 we are going to learn ways to organize and d