Name:
ID:
Homework 1 Solutions
1. [4-6] Let X be a continuous random variable with probability density
function f (x) = 2x, 0 x 1.
(a) Find E[X].
(b) Find E[X 2 ].
(c) Find Var[X].
(a) We have
E[X] =
(
1
x 2x dx =
xf (x) dx =
0
2x3
3
)
1
=
0
2
.
3
(b) We

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Homework 4 Solutions
First Midterm Exam:20/2/15
1. [8-13] In Example D of Section 8.4, the pdf of the population distribution
is
1 + x 1 x 1
2
f (x|) =
,
1 1,
0
otherwise
and the method of moments estimate was found to be = 3X (where X
is the s

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Quiz 4
1. A coin is thrown independently 20 times to test the null hypothesis that
the probability of heads is 0.5 versus the alternative hypothesis that the
probability is 0.4 . Let X be the number of heads. The test rejects H0 if
X 6.
a. What

Name: ID:
Quiz 5
1‘ A certain type of ﬂashlight is sold with the four batteries included. A
random sample of 150 ﬂashlights is obtained, and the number of defective
batteries in each is determined, resulting in the following date:
Let X be the numbe

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Homework 2 Solutions
1. [5-26] Suppose that a basketball player can score on a particular shot
with probability .3. Use the central limit theorem to nd the approximate distribution of S, the number of successes out of 25 independent
shots. Find

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Homework 5 Due date: 3/16/15
1. The drying time of a certain type of paint under specied test conditions is
known to be normally distributed with mean value 75 min and standard
deviation 9 min. Chemists have proposed a new additive designed to
d

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Homework 3 Solutions
1. [6-4] Let X1 , X2 , . . . , X8 be i.i.d. normal random variables with mean
and standard deviation . Dene
X
,
T =
S 2 /n
where X is the sample mean and S 2 is the sample variance.
(a) Find 1 such that P(|T | < 1 ) = .9;

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Homework 7 Due date: 4/17/15
1. A study was done to compare the performances of engine bearings made
of dierent compounds (McCool 1979). Ten bearings of each type were
tested. The following table gives the times until failure (in units of millio

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Homework 6 Due date: 3/27/15
Second midterm exam: 3/30/15
1. Let X1 , . . . , Xn be a random sample from a normal distribution N (X , 2 ),
and Y1 , . . . , Ym be a random sample from a normal distribution N (Y , 2 ),
with X , Y and unknown. We a

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STT442m Quiz 3
1. Assume X1, . . . ,Xn of iid. of random variables with density function
1 i931
f(a:ia):———exp —— , woo<zc<oo, a>0.
2a 0' ‘ _ _ .
Show that T(X1, . . . ,Xﬂ) m 2331 \Xﬁ-g is a sufﬁcient- statistic for (r.
a M
w:
W‘
“T”: \ EM

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Quiz 2
1. A random variable whose natural logarithm follows a normal distribution
is called a lognormal random variable. In particular, if Z N (0, 1), then
X = e+Z is a lognormal random variable with parameter and . The
pdf of X is
(ln x )2
1

STT 200 - STATISTICAL METHODS
LECTURE 002
HOMEWORK ASSIGNMENT NUMBER 4
DUE DATE: MONDAY NOVEMBER 28, 2016
Scantrons for Homework Assignment Number 4 will be passed out during the
class meeting of Wednesday November 23, 2016.
Each questian in this assignme

Central Limit Theorem (5.3)
Let X1 , X2 , . . . be a sequence of independent random variables, each having
n
mean and variance 2 . Then the distribution of the partial sum Sn =
Xi
i=1
becomes approximately normal with mean n and variance n 2 as n , that
i

Name:
PID:
STT4421 Second Midterm Exam
This is a 50-minute exam. You can not use any material except a notesheet.
Calculators are permitted, but other electronics are prohibited.
1. Let X1 , . . . , X100 be a random sample from a Poisson distribution with

General hypothesis testing (9.1 9.2)
A hypothesis is a statement about the population distribution.
If a hypothesis completely species the distribution, it is called a simple
hypothesis. (e.g. = 0 .)
If a hypothesis partially species the distribution, i

Central Limit Theorem (5.3)
Let X1 , X2 , . . . be a sequence of independent random variables, each having
n
mean and variance 2 . Then the distribution of the partial sum Sn =
Xi
i=1
becomes approximately normal with mean n and variance n 2 as n , that
i

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ID:
Quiz 4
1. The ratio of strength to cross sectional area for knee extensors is given in
the table taken from the article Knee Extensor and Knee Flexor Strength:
Cross Sectional area Ratios in Young and Elderly Men (J. of Gerontology,
1992). We as

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ID:
Quiz 4
1. During each of four experiments on the use of carbon tetrachloride as a
worm killer, ten rats were infested with larvae (Armitage 1983). Eight
days later, ve rats were treated with carbon tetrachloride; the other ve
were kept as contro

Final Examination Practice Sheet 1
STT 200 _. STATISTICAL METHODS
Lecture 2
FALL 2016
o Exercises on Sampling Distribution for One Sample Proportion
QUESTIONS 1 _ 2
Information on a packet of seeds claims that the germination rate is 84%. The packet conta

Final Examination Practice Exercises Sheet 11
STT 200 . STATISTICAL METHODS
Lecture 2
FALL 2016
PART I:
0 Confidence Intervals For One Sample Proportions
a Condence Intervals For The Difference Between Two Sample Proportions
1. A pollster Wishes to estima

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PID:
STT4421 First Midterm Exam
This is a 50-minute exam. You can not use any material except a notecard.
Calculators are permitted, but other electronics are prohibited.
1. [10pts] An insurance company has 10,000 automobile policyholders. The
expec