Homework 2 STAT 447 Fall 2013
Due 9/12 (R)
SOLUTION
PROBLEM 1 (30 pts)
Let [ X = 1] denote the event that a person is ultimately determined by experts with
certainty to have diabetes , and Let [ X = 0] denote the event that a person is ultimately
determin
Homework 1
STAT 447
Fall 2013
Due 9/4(W)
SOLUTION
Problem 1 (30pts) [See Problem 2.57 on p.60 of the book.] The probabilities that the serviceability of a
new X-ray machine will be will be rated by an X-ray technician as very difficult (=5), difficult (=4
Homework 1
STAT 447
Fall 2013
Due 9/4(W) Name_
NOTE: Your solution to each part of each problem MUST be located in the space just beneath that
part. If it is not located there, then it will not be acknowledged. I try to include more than enough
space for
Homework 2 STAT 447 Fall 2013
Due 9/12 (R)
Name _
PROBLEM 1 (30 pts)
Let [ X = 1] denote the event that a person is ultimately determined by experts with
certainty to have diabetes , and Let [ X = 0] denote the event that a person is ultimately
determined
Homework 6 Fall 2013 STAT 447
Due 11/7(R)
SOLUTION
PROBLEM 1.(15 pts) Book Problem 11.30 on p. 371 The length of the skulls of 10 fossil skeleton of an extinct
species of bird has a mean of 5.68 cm and a standard deviation of 0.29 cm. Assuming that such m
@VV i=9?
\ aa
\C\
1.
93 cfw_ (11
STAT 447 Practice Problems 2
We roll a pair of dice, one red and one green. (The different colors are used . (AI)
to emphasize that the dice are distinct from one another). Now, dene:
A 2 cfw_at least one of them wi
Name:
PID:
Practice problem 10
1. Let X1 , . . . , X25 be a random sample from a population with the following distribution
P(X1 = 0) = p,
P(X1 = 1) = 1 p,
where p is an unknown parameter. Consider the hypotheses
H0 : p = 0.6
versus
HA : p = 0.8.
(a) Show
Practice Problems 6
Practice Problem 6, Question 1: When circuit boards used in the manufacture of compact disc
players are tested, the long-run percentage of defectives is 5%, let X=the number of defective boards in
a random sample of size, so X~Bin(25,
._._3-
4L (7L 2L 9
gvi, / 5/ C( 3 29.1 fEhe sponsor has eight different commercials, each to be shown once? 8 (
m%m
"\
. Suppose a TrueFalse test has 20 questions.
. In how many ways may a student mark the test, if 6 questions are marked
. In how many w
"
Name: PID:
STAT 447 Practice Problems 4
1. A Pareto random variable X has the following PDF:
kc '
_ EFF 1f :13 Z 0
m _
fX( ) cfw_0, if a: < a
Wher eka n.nsreood0>OAwethfllWingque esiot
)Fi nedth value ofc
)Fi nedth CDF o,fX thatis IP(X<33)
CC 1: 2:3: M
g (Ii/2,5 ,3 STAT 447 Practice Problems 3
/
( / 9 ) ( l 5.) (1) The computers of ve faculty members in a statistics department are to
/ I be replaced. Two of the faculty members have selected laptop machines
(g?)/ C % U) and the other three have chosen de
.7 "; A statistical hypothesis, orjust hypothesij'is a claim about the value of a single '
parameter.
Specieg
% If a statistical hypothesis completely We Claim:
distribution, it is called a simple hypothesis; if not, it is . u at 0
referred to as a compos
Chapter 11: Interval Estimation
11.1: Introduction
0 Point estimation gives us a particular value as an estimate of the Population parameter.
0 Interval estimation gives us a range of values which likely to contain the Population parameter. This
interval
Name: ID:
STAT 447 Final Exam
1. [25 points] Let X1 . X100 be a random sample from a Poisson distribution with parameter
A, and consider the hypotheses
Ho : A = 0.02 versus HA : A = 0.04.
(a) Show that the likelihood ratio test is equivalent to the test w
ask A
w OK
(9,
Chapter 10: Point Estimation W W g \W Van
ViA KM \(i
(M yaw
Point Estimation
(Chapter 10)
Problems of
Estimation
Problems of Statistical Interval Estimation
Inference (Chapter 11)
Tests of Hypotheses
(Chapter 1
1
Homework 4
STAT 447 Fall 2013 Due 10/15(T)
Name_
Problem 1(15 pts) The meaning of the Coefficient of Determination, R 2:
From: http:/en.wikipedia.org/wiki/Coefficient_of_determination
A data set has values yi, each of which has an associated modeled val
1
Homework 5 STAT 447 Fall 2013 Due 10/24 (R)
SOLUTION
Problem 1 (20pts) Consider X ~ Bernoulli(p).
(3pts) Use the general formula E[ g ( X )] =
g ( x) f
X
SX
( x)dx to show that the mean and variance of X are
2
X = p and X = p(1 p) .
Solution:
n
(b)(6p
1
Homework 4 STAT 447 Fall 2012 Due 10/15(T)
Solution
Problem 1(15 pts) The meaning of the Coefficient of Determination, R 2:
From: http:/en.wikipedia.org/wiki/Coefficient_of_determination
A data set has values yi, each of which has an associated modelled
Homework 4
STAT 447 Fall 2013 Due 9/24(T)
Name_
PROBLEM 1.(ref. 5.43) (10 pts) In a certain city, 70% of all divorces claim incompatibility as the legal
reason. Use the Binomial pdf to find the probability that 5 of the next 6 cases claim incompatibility.
Homework 3
STAT 447 Fall 2013 Due 9/24(T)
Name_
PROBLEM 1.(ref. 5.43) (10 pts) In a certain city, 70% of all divorces claim incompatibility as the legal
reason. Use the Binomial pdf to find the probability that 5 of the next 6 cases claim incompatibility.
Chapter 2: Probability
Sample Space:
Denote as
Definition 2.1: The set of all possible outcomes of an experiment is called the Sample Space.
Example 2.1: Toss a coin - Head, or Tail, S = cfw_,
Example 2.2: Roll a dice - 1, 2, 3, 4, 5,6, S = cfw_1,2,3,4,
Chapter 1: Introduction
1.1 Combinatorial methods
In many problems of statistics, we must list all the alternatives that are possible in a given
situation or at least determine how many different possibilities there are.
Theorem 1.1 If an operation consis
Hyper Geometric
5.2: The Discrete Uniform Distribution
If a random variable can take on k different values with equal probability, we say that it has a discrete
uniform distribution.
Definition 5.1:
A random variable X has a discrete uniform distribution,
Practice problems in class 9
(1-5) Let 1 , 2 , 3 200 be independent random variables with the exponential
distributions (=0.1).
Define =
1 + 2 + 3+ +200
200
and T=1 + 2 + 3+ + 200 .
Answer the following question:
1. Find the E[3 ] and SD[3 ] .
2. What is
Chapter 13: Test of Hypothesis
: average of population
2: variance of population
Normal
Non-normal
Known
Unknown
STEP 1
Hypothesis
Known
: = . : <
: = . :
Unknown
Known
Unknown
Normal
(Distribution)
(p359)
Non-normal
(Distribution)
Normal
(Distributi
Practice Problems 7
Practice Problem 7, Question 1: A package delivery service divides their packages into weight classes.
Suppose that packages in the 14 to 20 pound class are uniformly distributed, meaning that all weights
within that class are equally