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