Probability
Table entry for z is
the area under the
standard normal curve
to the left of z .
z
TABLE A Standard normal probabilities
z
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
MAT 281
Introduction to Probability
Homework Assignment 1 Answer Key
(1) Suppose a family contains two children of different ages, and we are interested in the
gender of these children. Let F denote that a child is female and M that the child
is male and
MAT 281
Introduction to Probability
Homework Assignment 1
(1) Suppose a family contains two children of different ages, and we are interested in the
gender of these children. Let F denote that a child is female and M that the child
is male and let a pair
MAT 281
Introduction to Probability
Fall 2012
Name:_
Exam 1
For full credit, show all of your works and use appropriate notation. Do not
simply write the final numerical answer. No credit for correct final answer
without a valid argument. Show your work g
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 4 (Part 2)
Continuous Random Variables and Their Probability
Distributions
Complementary reading (Chapter 4 WMS)
AbouEl-Makarim
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 4 (Part 1)
Continuous Random Variables and Their Probability
Distributions
Complementary reading (Chapter 4 WMS)
AbouEl-Makarim
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 3 (part 3)
Discrete Random Variables and Their Probability
Distributions
Complementary reading (Chapter 3 WMS)
AbouEl-Makarim A
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 3 (part 2)
Discrete Random Variables and Their Probability
Distributions
Complementary reading (Chapter 3 WMS)
AbouEl-Makarim A
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 3 (part 1)
Discrete Random Variables and Their Probability
Distributions
Complementary reading (Chapter 3 WMS)
AbouEl-Makarim A
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 2
Probability (Some Proofs)
Complementary reading (Chapter 2 WMS)
AbouEl-Makarim Aboueissa, Ph. D.
B
A
A BC
AC B
A B
S
Copyrigh
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 2
Probability
Complementary reading (Chapter 2 WMS)
AbouEl-Makarim Aboueissa, Ph. D.
Experiment
Any activity that yields a resu
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 1 (part 1)
Descriptive Statistics
Complementary reading (Chapter 1 WMS)
AbouEl-Makarim Aboueissa, Ph. D.
Objectives of Statisti
AbouEl-Makarim A. Aboueissa, Ph.D.
Department of Mathematics and Statistics, USM
MAT 281
Introduction to Probability
On Chapter 1 (part 2)
Descriptive Statistics
Complementary reading (Chapter 1 WMS)
AbouEl-Makarim Aboueissa, Ph. D.
Frequency Distribution
MAT 282
Statistical Inference
Spring2012
Instructions for Exam 1
Due date: Your exam must be returned to me by or before 12:00 P.M.
on Tuesday, March 6, 2012.
Keep your test paper confidential: You may discuss your solution with
other students and even sh
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 10
(1)
Let
Y1 , Y2 ,.,Yn be a random sample from a N ( , 2 ) distribution, where 2 is
known. The following two simple hypotheses are being tested:
H 0 : = 0 versus H a : = a
where
a < 0
(a) Fin
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 9
(1) Define
and
for a statistical test of hypotheses.
(2) An experimenter has prepared a drug dosage level that she claims will induce
sleep for 80% of people suffering from insomnia. After e
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 8
(1) Let Y1, Y2 ,., Yn
denote a random sample from the density function given by:
1 r 1 y r
, > 0, y > 0
ry e
f ( y | ) =
0,
elsewhere
where
r
is a known positive constant.
(a) Find a suff
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 7
(1) Let Y1, Y2 ,., Yn
denote a random sample from a normal distribution with
2
mean and variance .
(a) If is unknown and 2 is known, show that Y is sufficient statistic for .
(b) If
is known
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 6
(1) The number of weekly breakdowns for a minicomputer is a random variable
Y with a Poisson distribution with mean . We will take a random sample
over n weeks and obtain Y 1,Y 2 ,.,Y n , a s
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 5
(1) Let Y1, Y2 ,., Yn
denotes a random of size
density function is given by:
y 1
,
f ( y) =
0,
n
from a population whose
0 y
elsewhere
Where
> 0 is known, fixed value, but is unknown. (Th
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 4
(1) A random sample of size 81 will be taken from a population with mean
= 128 and standard deviation = 6.3 . What is the approximate
probability that the sample mean will fall between 126.6
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 3
(1) Suppose that X1, X 2 ,., X n
and
Y1, Y2 ,., Yn are independent random
samples from populations with means 1 and
respectively. Show that the random variable
Un
2
2
2 and variances 1 and 2
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 2
(1) Let Y 1,Y 2 ,.,Y n be independent uniformly distributed random variables on
the interval [0, ] . Find the
(a) Cumulative Distribution Function (CDF ) of Y ( n ) = max(Y 1 ,Y 2 ,.,Y n ).
(
MAT 282
Statistical Inference
Spring 2012
Homework Assignment 1
(1) If the joint density of Y 1 and Y 2
is given by:
f ( y 1, y 2 ) = e ( y 1 + y 2 )
for
y 1 > 0, y 2 > 0
and
U=
Y 1 +Y 2
2
find the density function of U using the method of Cumulative Dist