STAT 3340 Assignment 1 solutions
(out of 125 points)
(10)
1. Find the equation of the line which passes through the points (1,1) and (4,5).
1 = (5 1)/(4 1) = 4/3
equation for the line is y y0 = 1 (x x0 ), where (x0 , y0 ) is a point on the line. Using the
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ermitted.
Please answer the questions in the space pr
the t with innite degrees
One sheet of formulae] notes. letter size. and a calculator are p
Tables are provided for t and F. For the normal distribution use
of freedo
Wmg
Student Number: _
STATISTICS 3340/ MATH 3340 Final Exam, Sat. Dec. 19. 2009
Please answer the questions in the space provided. Justify your answers.
Three sheets of formulae/notes. letter size, are permitted.
1. A data set contains information on the
Assignment 1, due Oct 2, 2015
(4)
1. Find the equation of the line which passes through the points (1,1) and
(3,5).
slope = rise/run, so slope = (5-1)/(3-1) = 2
y-intercept is -1, because a decrease in 1 in the horizontal direction
leads to a change of
Assignment 3, due Oct. 28 2015 Solutions
1. In assignment 2 you worked with data on fish lengths, with age and water
temperature as predictors. We saw that there was curvature in the
residual plots, and so the full quadratic model
y = 0 + 1 x1 + 2 x2 + 3
Assignment 6, due Dec. 7, 2015 Solutions
1. We have fitted the model
loss = 0 +1 Air.F low+2 Acid.Conc+3 W ater.T emp+4 W ater.T emp2 +
(3)
(a) Obtain the leverage values for this model. Are any above the usual
cutoff of 2p/n? If so, explain why this case
Assignment 2, due Oct. 21 2015 SOLUTIONS
The length of a species of fish is to be represented as a function of the age and water
temperature. The fish are kept in tanks at 25, 27, 29 and 31 degrees Celsius. After
birth, a test specimen is chosen at random
Assignment 5, due Nov. 27 2015
1. In assignment 2 and 3 and 4 you worked with data on fish lengths, with
age and water temperature as predictors. You have now fitted a
quadratic model
y = 0 + 1 x1 + 2 x2 + 3 x1 x2 + 4 x21 + 5 x22 +
(6)
(a) Determine whet
MATH/STAT 3360, Probability
FALL 2015
Sample Final Examination
Model Solutions
This Sample examination has more questions than the actual final, in order
to cover a wider range of questions. Estimated times are provided after each
question to help your pr
MATH/STAT 3360, Probability
FALL 2015 Hong Gu
Homework Sheet 2
Model Solutions
Basic Questions
1. What is the probability that the sum of 3 fair 6-sided dice is 8?
The following possibilities sum to 8: (1,1,6), (1,2,5), (1,3,4), (1,4,3), (1,5,2),
(1,6,1)
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 1
Model Solutions
Basic Questions
1. A statistics textbook has 10 chapters. Each chapter has 20 questions and
each question has 3 parts. How many part-questions are there in total in
the book?
T
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 7
Due: Thursday 26th November: 2:30 PM
Basic Questions
1. If X is exponentially distributed with parameter and Y is normally
distributed with mean 0 and variance 2 ,
(a) nd the moment generating
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 5
Due: Tuesday 27th October: 2:30 PM
Basic Questions
1. If X is normally distributed with mean 0 and variance 1, what is the
probability density function of X 2 ?
2. Let X be normally distribute
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 4
Due: Thursday 15th October: 2:30 PM
Basic Questions
1. A random variable X has the following probability mass function:
x P (X = x)
0 0.1
1 0.2
3 0.3
4 0.2
7 0.1
20 0.1
(a) What is E(X)?
(b) W
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 2
Due: Thursday 1st October: 2:30 PM
Basic Questions
1. What is the probability that the sum of 3 fair 6-sided dice is 8?
2. For an experiment with sample space cfw_1, 2, 3, 4, 5, is there a pro
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 1
Due: Thursday 24th September: 2:30 PM
Basic Questions
1. A statistics textbook has 10 chapters. Each chapter has 20 questions and
each question has 3 parts. How many part-questions are there i
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 8
Due: Thursday 3rd December: 2:30 PM
Basic Questions
Homework 7, Q.1 If X is exponentially distributed with parameter and Y is normally
distributed with mean 0 and variance 2 ,
(b) Use the Cher
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 6
Due: Thursday 19th November: 2:30 PM
Basic Questions
1. X is normally distributed with mean 5 and standard deviation 1. Y is
independent and normally distributed with mean 2 and standard devia
MATH/STAT 3360, Probability
FALL 2015
Hong Gu
Homework Sheet 3
Due: Thursday 8th October: 2:30 PM
Basic Questions
1. Three fair dice are rolled. Which of the following pairs of events are
independent?
There is exactly one 6 among
(a) The rst roll is 6.
th
STAT 3460 - Lecture 21
Tests for Binomial Probabilities - 12.4
March 21, 2012
Tests of Signicance
Tests for Binomial Probabilities
Consider an experiment where k treatments are compared on the
basis of success/failure data with the results tabulated below
STAT 3460 - Lecture 25
Tests of Signicance: Signicance Regions - 12.9
March 30, 2012
Signicance Regions
Signicance Regions - 12.9
Condence Interval Construction based on Tests of Signicance.
For a test of H : = 0 , the signicance level will depend on
the
STAT 3460 - Lecture 24
Cause and Eect - 12.7
Tests for Marginal Homogeneity - 12.8
March 28, 2012
Cause and Eect
Association versus Cause and Eect
Earlier, when the hypothesis of independence was tested
and a small signicance level observed, we noted obse
STAT 3460 - Lecture 18
Tests of Signicance - 12.1
March 12, 2012
2 () and Exponential Distributions
Show that if X is Exponentially distributed
with mean , then 2X is 2 (2) distributed
Let Y 2X /, where f (x) = (1/) e x/
For variable transform: g (y ) = f
STAT 3460 - Lecture 22
Tests for Multinomial Probabilities - 12.5
March 23, 2012
Tests of Signicance
Tests for Multinomial Probabilities - 12.5
Suppose we have n repetitions of an experiment and that we wish
to assess how well the data agree with an hypot
STAT 3460 - Lecture 20
Likelihood Ratio Tests: Composite Hypotheses 12.3
March 19, 2012
Tests of Signicance
Likelihood Ratio Test: Composite Hypothesis
Hypothesized Model: Consists of both the basic probability
model for the experiment and a hypothesis re
STAT 3460 - Lecture 19
Likelihood Ratio Tests: Simple Hypotheses - 12.2
March 16, 2012
Tests of Signicance
Likelihood Ratio Tests
Likelihood Ratio Statistic: When hypotheses can be
formulated as an assertion of the value of unknown
parameters in a probabi
STAT 3460 - Lecture 23
Tests for Independence: Contingency Tables 12.6
March 23, 2012
Tests for Independence
Cross-Classied Data
Study to evaluate three cancer treatments classifed n patients
according to treatment and survival.
Resulting frequencies, fij
STAT 3460 - Lecture 15
Chi-Square Approximation - 11.3
February 27, 2012
Frequency Properties
Coverage Probability for Likelihood Intervals
The 100p% LI for is the set of values where r () log (p).
0 belongs to the 100p% LI for if and only if r (0 ) log (
STAT 3460 - Lecture 17
Two Parameter Models - 11.5
March 17, 2011
Frequency Properties
Two Parameter Models
Here we consider probability models with two unknown
parameters, and .
As before, r (, ) denotes the joint log RLF of and .
The 100p% likelihood re
STAT 3460 - Lecture 16
Condence Intervals - 11.4
February 29, 2012
Frequency Properties
Condence Intervals
A random interval [A, B] is called a condence interval for if
its coverage probability is the same for all parameter values 0 .
CP(0 ) = P(A 0 B | =