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
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
X1 = 1 / 2n ( Xi )
X2 = 1 / n ( X i )
1 Empirical Models
Many problems in engineering and science involve
exploring the relationships between two or more
Regression analysis is a statistical technique that is
very useful for these types of problems.
Topic 7: Statistical Intervals for
a Single Sample
a) Confidence Interval on the Mean of a Normal
b) Confidence Interval for Variance and Standard
c) Confidence Interval for a Proportion
In the previous topic we i
CHE220, Tutorial 1: Set Operations, Counting, and Definition of Probability
Represent the following sets by listing all their elements.
cfw_ x : x is a positive integer, x 12
cfw_ x : x is the square of a positive integer, x < 100
cfw_ x : x
Workshop 4: Simple Linear Regression and Correlation
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
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
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
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
Treatment of Data
Data Summary and Display
Time Sequence Plots
1 Data Summary and Display
1 Data Summary and Display
1 Data Summary
H.W. # 1 (Due Thursday October 4, 2012)
(Submit only problems marked with a *)
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
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
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
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.
H.W. 4 Solutions
1 E X = 1 ( 2n ) =
E X 1 = E i =1 =
2n i =1 2n
E X 2 = E i =1 = E X i = ( n ) = ,
n i =1 n
The variances are V X 1 =
X 1 and X 2 are unbiased estimators of .
and V X 2 =
; compare th
H.W. 2 - Solutions
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
Mean and Variance
HW 6 - Due on December 6, 2012
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.
(a) Is there evidence to s
H.W. 1 - Solutions
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,
c) 11 < X