CHE220, Tutorial 3: Probability mass function, cumulative distribution function, mean and
variance of a discrete random variable, discrete uniform distribution
Problem 1: Marketing estimates that a new instrument for the analysis of soil samples will be
v
H.W. # 4 (Due Thursday, November 15, 2012)
(Note: submit only problems marked with a *)
1) * Suppose we have a random sample of size 2n from a population denoted by X, and
E(X) = u and V(X) = 2. Let
_
2n
X1 = 1 / 2n ( Xi )
i=1
_
n
X2 = 1 / n ( X i )
i=1
b
Curve Fitting
1
1 Empirical Models
Many problems in engineering and science involve
exploring the relationships between two or more
variables.
Regression analysis is a statistical technique that is
very useful for these types of problems.
For example,
Topic 7: Statistical Intervals for
a Single Sample
a) Confidence Interval on the Mean of a Normal
Population.
b) Confidence Interval for Variance and Standard
Deviation
c) Confidence Interval for a Proportion
1
7-1 Introduction
In the previous topic we i
CHE220, Tutorial 1: Set Operations, Counting, and Definition of Probability
1.
Represent the following sets by listing all their elements.
a)
cfw_ x : x is a positive integer, x 12
b)
cfw_ x : x is the square of a positive integer, x < 100
c)
cfw_ x : x
Workshop 4: Simple Linear Regression and Correlation
Instructions:
In this workshop you will apply regression analysis tools available in Excel to describe a
manufacturing process after a new management program has been implemented. You will
examine vario
CHE220, Workshop 3: Statistical Intervals for a Single Sample
I. Confidence Interval on Mean, Variance Unknown
When working with a data sample of a particular measurement taken from a population, you
can estimate the mean and variance of that parameter in
Tutorial 7 - Hypothesis Testing
Solutions
Problem 1: The Naphtha reformer unit in a refinery produces an octane number of 90
under an existing (old) catalyst. A new catalyst has been developed and used in the unit.
An average octane number of 92 has been
CHE220, Tutorial 5: Continuous Random Variables and Probability Distributions
1. The probability density function of the net weight in pounds of a packaged chemical
herbicide is f(x) = 2.0 for 49.75 < x < 50.25 pounds.
(a) Determine the probability that a
CHE220, Tutorial 6: Point Estimation of Parameters, Statistical Intervals for a Single
Sample
Problem I: An engineer is analyzing the compressive strength of concrete. Compressive
strength is normally distributed with 2 = 1000 (psi)2. A random sample of 1
CHE220, Tutorial 4: BINOMIAL & POISSON DISTRIBUTION
Problem 1: In inspecting 1450 welded joints produced by a certain type of welding machine,
168 defective joints were found. In welding five joints, what is the probability of getting
0,1,2,3,4,5, defecti
Treatment of Data
Outline:
1.
2.
3.
4.
5.
6.
Data Summary and Display
Random Sampling
Stem-and-Leaf Diagram
Box Plots
Time Sequence Plots
Probability Plots
1
1 Data Summary and Display
Definition
(1)
2
1 Data Summary and Display
Example 1
3
1 Data Summary
H.W. # 1 (Due Thursday October 4, 2012)
(Submit only problems marked with a *)
Problem 1:
A digital scale is used that provides weights to the nearest gram.
(a) What is the sample space for this experiment?
Let A denote the event that a weight exceeds 11
Theory
Oxidation-reduction reactions, or redox reactions, are volumetric analytical methods that
can analyze more species than other methods, such as acid-base or precipitation reactions. A
notable application of redox methods is to determine the amount o
PRELAB THEORY
The purpose of this lab is to use filtering techniques such as with filter funnels and filter flasks to
gravimetrically determine the unknown percentage amount of calcium. An unknown J series will be
given in calcium carbonate form that will
Testing for Goodness of Fit
The test is based on the chi-square distribution.
Assume there is a sample of size n from a population whose probability distribution is
unknown.
Let Oi be the observed frequency in the ith class interval.
Let Ei be the expecte
CHE220, Tutorial 2: Addition Rules, Conditional Probability, Total Probability,
Independence, Bayes Theorem
1. The analysis of shafts for a compressor is summarized by conformance to specifications.
roundness conforms
yes
surface finish
conforms
yes
no
no
H.W. 4 Solutions
1)
2n
Xi
2n
1 E X = 1 ( 2n ) =
i
E X 1 = E i =1 =
2n
2n i =1 2n
n
Xi
n
1
1
E X 2 = E i =1 = E X i = ( n ) = ,
n
n i =1 n
()
()
()
The variances are V X 1 =
X 1 and X 2 are unbiased estimators of .
()
2
2
and V X 2 =
; compare th
H.W. 2 - Solutions
1.
The sum of the probabilities is 1 and all probabilities are greater than or equal to zero;
pmf: f(1) = 0.7, f(4) = 0.2, f(7) = 0.1
a) P(X 4) = 0.9
b) P(X > 7) = 0
c) P(X 5) = 0.9
d) P(X>4) = 0.1
e) P(X 2) = 0.7
2.
Mean and Variance
HW 6 - Due on December 6, 2012
Problem 1:
An article in Concrete Research (Near Surface Characteristics of Concrete: Intrinsic
permeability, Vol. 41, 1989), presented data on compressive strength x and
intrinsic permeability y of various concrete mixes an
HW 5 - Due Tuesday, November 27, 2012
1. The compressive strength of concrete is being tested by a civil engineer. He tests 12
specimens and obtains the following data.
2216
2225
2318
2237
2301
2255
2249
2281
2275
2204
2263
2295
(a) Is there evidence to s
H.W. 1 - Solutions
1.
a) S = nonnegative integers from 0 to the largest integer that can be displayed by the scale.
Let X represent weight.
A is the event that X > 11
B is the event that X 15
C is the event that 8 X <12
S = cfw_0, 1, 2, 3,
b) S
c) 11 < X