1
1-1 The Engineering Method and Statistical Thinking
An engineer is someone who solves problems of interest to society by the efficient application of scientific principles by Refining existing products Designing new products or processes
1-1 The Enginee

EIN 3235 Mid-term Exam (Spring 2010) PantherID: Name:
Instruction: Your can submit printed or hand-written solution on class. Alternatively, solution can be submitted via email to zzhai001@fiu.edu; please make sure that you get confirmation of receipt fro

Exercises for Section 2.1
6. In a laboratory test of a new engine design, the
emissions rate (in mg/s of oxides of nitrogen,
NOX) was measured as a function of engine
speed (in rpm). The 8 results are presented in
the following table.
Speed
Emissio
ns
167

Final exam for EIN 3235 Spring 2010 Panther ID: Name:
Instruction: Solution should be submitted (1) via email to zzhai001@fiu.edu; please make sure that you get confirmation of receipt from the instructor. Or (2) submit hard copy in person The deadline of

2-1 Sample Spaces and Events
2-1.1 Random Experiments
Figure 2-1 Continuous iteration between model and physical system.
2-1 Sample Spaces and Events
2-1.1 Random Experiments
Figure 2-2 Noise variables affect the transformation of inputs to outputs.
2-1 S

Exercises for Section 1.2
10. A sample of 100 adult women was taken, and
each was asked how many children she had.
The results were as follows:
Children
0
1
2
3
4
5
Number
27
22
30
12
7
2
of
Women
a. Find the sample mean number of children.
b. Find the sa

Chapter 3:
Probability
1
Section 3.1: Basic Ideas
Definition: An experiment is a process that
results in an outcome that cannot be predicted
in advance with certainty.
Examples:
rolling a die
tossing a coin
weighing the contents of a box of cereal.
2
Samp

Chapter 5:
Point and Interval Estimation
for a Single Sample
1
Introduction
When data is collected, it is often with the
purpose of estimating some characteristic
of the population from which they came.
The sample mean and sample proportion
are examples

Chapter 6:
Hypothesis Testing
1
Introduction
Recall: We discussed an example in Chapter 5 about
microdrills.
Our sample had a mean of 12.68 and standard
deviation of 6.83.
Let us assume that the main question is whether or
not the population mean lifet

Chapter 7:
Inferences for Two Samples
1
Introduction
In Chapters 5 and 6, we saw how to
construct confidence intervals and perform
hypothesis tests concerning a single mean
or proportion.
There are cases in which we have two
populations, and we wish to

Chapter 8:
Inference in Linear Models
1
Introduction
We discussed bivariate data in Chapter 2.
In this chapter, we learn to compute confidence
intervals and to perform hypothesis tests on the slope
and intercept of the true regression line.
We have tal

Chapter 9:
Factorial Experiments
1
Section 9.1: One-Factor
Experiments
In general, a factorial experiment involves several
variables.
One variable is the response variable, which is
sometimes called the outcome variable or the
dependent variable.
The o

*Attn: the formula given by the textbook only apply for consecutive integers (a) P(X>20)=P(X=21)+ P(X=22)+ P(X=23)+ P(X=24)+ P(X=25) =9.67E-10 0 Excel: =1-P(X<=20)=1-binomdist(20,25,0.25,true)
Excel: =P(X<=4)=binomdist(4,25,0.25,true)

3-1 Discrete Random Variables
3-1 Discrete Random Variables
Example 3-1
3-2 Probability Distributions and Probability Mass Functions
Figure 3-1 Probability distribution for bits in error.
3-2 Probability Distributions and Probability Mass Functions
Figure

4-1 Continuous Random Variables
4-2 Probability Distributions and Probability Density Functions
Figure 4-1 Density function of a loading on a long, thin beam.
4-2 Probability Distributions and Probability Density Functions
Figure 4-2 Probability determine

5-1 Two Discrete Random Variables
Example 5-1
5-1 Two Discrete Random Variables
Figure 5-1 Joint probability distribution of X and Y in Example 5-1.
5-1 Two Discrete Random Variables
5-1.1 Joint Probability Distributions
5-1 Two Discrete Random Variables

6-1 Numerical Summaries
Definition: Sample Mean
6-1 Numerical Summaries
Example 6-1
6-1 Numerical Summaries
Figure 6-1 The sample mean as a balance point for a system of weights.
6-1 Numerical Summaries
Population Mean For a finite population with N measu

7-1 Introduction
The field of statistical inference consists of those methods used to make decisions or to draw conclusions about a population. These methods utilize the information contained in a sample from the population in drawing conclusions. Statis

9-1 Hypothesis Testing
9-1.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval estimation of parameters are the fundamental methods used at the data analysis stage of a comparative experiment, in which the engineer is intereste

Minitab Steps Problem 1: With the following sample GPA, we are 95% that FIU student GPA is between ? and ? 3.1 3.2 3.3 3.4 Assume FIU GPA has standard deviation=0.01 Solution: It is to find two-sided Confidence Interval with known variance. Step1: use 1 s

Comments: If we recall exponential distribution, f(x) is an exponential pdf. User Y=X-4
Comments: we should also include F(x)=0
x<=4
Comments: for (e) P(-x/4<Z<x/4)=P(Z<x/4)- P(Z<-x/4) here we use formula P(Z<-a)=1P(Z<a) Then we have 2P(Z<x/4)-1=0.99 P(Z<

Solution for Mid-term exam
1. P(AB)=P(A)+P(B)-P(AB)= P(A)+P(B)=0.5 (as no sharing indicates P(AB)=0). similarly, P(CB)= P(C)+P(B)=0.75 Also food can only be seized by one fish, either A, B, or C, i.e. P(A)+P(B)+P(C)=1. By solving these three equations, we

Chapter 10:
Statistical Quality
Control
1
Introduction
As the marketplace for industrial goods has become
more global, manufacturers have realized that quality
and reliability of their products must be as high as
possible for them to be competitive.
It