ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Tuesday, March 22, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 17: The 2p factorial design
The 2p factorial design an
ST2131/MA2216
Semester II, 2016/2017
Tutorial 3 Solution
1. Let S = cfw_1, 2, . . . , n and suppose that A and B are, independently, equally likely to be any of the 2n
subsets (including the null set and S itself) of S.
(a) Show that
n
3
.
P (A B) =
4
Hi
ST2131/MA2216
Semester II, 2016/2017
Tutorial 4 Solution
1. Suppose we have an urn containing b blue balls, g green balls and r red balls. We draw balls one at a
time, without replacement. Let Pk be the probability that the first non-red ball that is draw
ST2131/MA2216
Semester II, 2016/2017
Tutorial 2 Solution
1. (a) Two cards are randomly selected from an ordinary playing deck. What is the probability that
they form a blackjack? That is, what is the probability that one of the cards is an ace and the
oth
ST2131/MA2216
Semester II, 2016/2017
Tutorial 1
1. Ten weight lifters are competing in a team weight-lifting contest. Of the lifters, 3 are from the United
States, 4 are from Russia, 2 are from China, and 1 is from Canada. Scoring takes account of the
cou
ST2131/MA2216
Semester II, 2016/2017
Tutorial 4
1. Suppose we have an urn containing b blue balls, g green balls and r red balls. We draw balls one at a
time, without replacement. Let Pk be the probability that the first non-red ball that is drawn is blue
ST2131/MA2216
Semester II, 2016/2017
Tutorial 1 Guided Questions
1. Consider n-digit numbers where each digit is one of the 10 integers 0, 1, . . . , 9. How many such numbers
are there for which
(i) no two consecutive digits are equal?
(ii) 0 appears as a
ST2131/MA2216
Semester II, 2016/2017
Tutorial 4 & 5 Guided Questions (Chapter 4)
1. Let Pn denote the probability that n Bernoulli trials result in an even number of successes (0 being
considered an even number). Show that
Pn = p(1 Pn1 ) + (1 p)Pn1 ,
n1
a
ST2131/MA2216
Semester II, 2016/2017
Tutorial 2 Guided Questions
1. In an experiment, a die is rolled continually until a 6 appears, at which point the experiment stops.
What is the sample space of this experiment? Let En denote the event that n rolls are
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Friday, April 1, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 19: Blocking and confounding in 2p factorial
designs
A g
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
2:00-4:00 pm, Monday, April 8, 2013
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 21: Fractional 2p factorial designs
The general principl
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Friday, March 11, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 14: Balanced incomplete block designs (BIBD)
What is BI
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Tuesday, March 15, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 15: Introduction to factorial designs
Factorial design
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Tuesday, March 29, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 18: The analysis of the data from 2p designs
The steps
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Tuesday, April 12, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 22: More on fractional 2p factorial designs
The one qu
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Tuesday, April 5, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 20: General blocking and partial confounding in 2p
fact
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Friday, February 19, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 11: Latin Square Design
Latin square design and its
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Tuesday, March 8, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 13: Graeco-Latin squares and application of Latin
squar
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Tuesday, March 1, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 12: Replicated Latin Squares Design
General remarks
I
R
ST3232: Design and Analysis of Experiments
Chen Zehua
Department of Statistics & Applied Probability
4:00-6:00 pm, Friday, March 18, 2016
Chen Zehua
ST3232: Design and Analysis of Experiments
Lecture 16: General p-factor factorial designs
The design
I
A p
ST2131/MA2216
Semester II, 2016/2017
Tutorial 1 Self Practice
1. Two experiments are to be performed. The first can result in any one of m possible outcomes. If the
first experiment results in outcome number i, then the second experiment can result in any
MA2216/ST2131 Probability Notes 9 Review & Examples and Properties of Expectation 1. Linear Transformation. Let X1 , X2 , . . . , Xn be continuous random variables having joint density f and let random variables Y1 , Y2 , . . . , Yn be defined by the foll
MA2216/ST2131 Probability Notes 8 Multidimensional Changes of Variables and Bivariate Normal Distribution 1. Changes of Variables Let X1 and X2 be jointly distributed random variables with joint probability density function fX1 ,X2 . It is sometimes neces
MA2216/ST2131 Probability Notes 7 Sums of Independent Random Variables Very often we are interested in the sum of independent random variables. When X and Y are independent, we would like to know the distribution of X + Y . In the following, we will deal
MA2216/ST2131 Probability Notes 6 Joint Probability Distributions So far, we have only considered probability distributions for single random variables. There will be situations, however, where we may find it desirable to record the simultaneous outcomes
MA2216/ST2131 Probability Notes 5 Distribution of a Function of a Random Variable We have seen that an "affine transformation" of a normal r.v. is still normally distributed. To be precise, let X N (, 2 ). Put Y = aX + b. Then, it has been pointed out in
MA2216/ST2131 Probability Notes 4 1. Discrete Uniform Distribution. 1. If X assumes the values x1 < x2 < . < xn , with equal probabilities, then X is called a discrete uniform r.v. The probability distribution of X is called the discrete uniform distribut
MA2216/ST2131 Probability Notes 3 1. Random Variables. It is frequently the case that, when an experiment is performed, we are mainly interested in some function of the outcome as opposed to the actual outcome itself. For instance, in testing 100 electron
MA2216/ST2131 Probability Notes 2 1. Axioms of Probability Consider an experiment whose sample space is S. The objective of probability is to assign to each event A a number IP(A), in [0, 1], called the probability of the event A, which will give a precis