STAT 630 Fall 2013
Homework 7 Solution
4.6.1
(a) Since X1 and X2 have the normal distributions and they are independent, thus U and
V are also normal random variables. Since E[U ] = 3 + 40 = 43, V ar(
630 homework7 solution
Editor:
4.6.1
(a). Since X1 and X2 have the normal distributions and they are independent, thus
U and V are also normal random variables. Since E [U ] = 3 + 40 = 43, V ar(U ) =
STATISTICS 630 - Solution to Test I
October 8, 2010
1. Suppose that we toss four fair coins.
(a) Find the probability of tossing exactly one head.
Let X = the number of heads. Then P (X = 1) =
4
1
0.5
630 Homework3 solution
2.4.2
(a). Since W is dened on interval [1, 4], thus P (W 5) = 0;
(b). P (W 2) =
4 2
4 1
2
= 3;
(c). P (W 2 9) = P (W 3) = 31 = 2 ;
1
4213
2 2) = P (W
2) = 41 =
(d). P (W
2 1
Problem 1.5.22
The attached system has ve components which act independently. Each
component fails with probability p. Find the probability that the system fails.
System with 5 Components
1
2
3
5
4
1
630 homework8 solution
Editor:
6.2.4
(a). Since f (xi ; ) =
n
e xi
xi ! ,
then we can write down the log-likelihood function: l(|X ) =
n
( + xi log () log (xi !) = n + log ()
i=1
n
xi
i=1
tive with r
STATISTICS 630 - Solution to Test II
July 15, 2011
1. Suppose that the amount of a metal alloy produced by a factory each week is uniformly
distributed between 40 kilograms and 64 kilograms, and that
630 Homework6 solution
3.5.4
First we need to obtain the marginal distribution of Y. From the joint distribution of X and Y in question
3.5.3, we can obtain: pY (2) =
2
11 , pY (3)
=
3
11 , pY (7)
=
5
STATISTICS 630 - Solution to Test I
June 21, 2011
1. Let A be the event that your right knee is sore on a given morning and B be the event
that your left knee is sore on that morning. Suppose that P (
STATISTICS 630 - Solution to Final Exam
December 14, 2010
1. Suppose that the time (in minutes) that a professor takes to grade a single nal exam is a
uniform random variable on the interval [6, 12].
STATISTICS 630 - Solution to Test II
November 12, 2014
1. The weight X (in pounds) of small packages (under 2 pounds) delivered by UPS is
assumed to be a random variable with probability density funct
STATISTICS 630 - Solution to Final Exam
December 13, 2016
1. Suppose that X1 , . . . , Xn is a random sample from a distribution with probability density function
cfw_
x x/
, 0 < x < ,
2e
fX (x) =
0,
STATISTICS 630 - Final Exam
December 10, 2013
Name
Email Address
INSTRUCTIONS FOR STUDENTS:
(1) There are 8 pages including this cover page and 5 formula sheets. Each of the six
numbered problems is w
STATISTICS 630 - Solution to Final Exam
December 15, 2015
1. Let X and Y be independent random variables where X has a normal distribution with
mean 2 and variance 6 and Y has a Poisson distribution w
STATISTICS 630 - Solution to Final Exam
December 16, 2014
1. Let X N (1, 4) and Y N (2, 8) be independent normal random variables. (Note:
The notation N (a, b) indicates a normal distribution with mea
STATISTICS 630 - Solution to Final Exam
December 10, 2013
1. Let X and Y be jointly distributed random variables with means X = 0 and Y = 2,
2
variances X
= 2 and Y2 = 4, and covariance Cov(X, Y ) = 1
STAT 630Formulas for Test 2
Cumulative Distribution Function
The cdf of a random variable X is a function FX (x) = P (X x) for each x.
Relationship of CDF and PDF for a Continuous RV: fX (x) =
d
F (x)
STATISTICS 630 - Test II
November 12, 2014
Name
Email Address
INSTRUCTIONS FOR STUDENTS:
(1) There are seven pages including this cover page and four formula sheets. Each of the
five numbered problems
Statistics 630
3 Expected Values
Expectations of a random variable
Expectation of a discrete rv
Expectation of a continuous rv
Expectations of functions of a rv
Properties of expectation
Expecta
STATISTICS 630 - Solution to Test II
November 9, 2017
1. Suppose that Z1 , Z2 , Z3 , Z4 , Z5 are independent standard normal random variables. Let
U = Z12 + Z22 and V = Z32 + Z42 + Z52 .
(a) Identify
Regression Analysis: STAT 608
Spring 2018, Sections 600 & 700, Texas A&M University, Department of Statistics
t is imperative that models be valid for
Explain and compare properties of summary and
an
STATISTICS 630 - Solution to Test II
November 11, 2015
1. In Test 1, you considered the joint probability mass function (pmf) pX,Y (x, y) for (X, Y ),
given in the following table:
0
1
x 2
3
pY (y)
0
STATISTICS 630 - Final Exam
December 13, 2016
Name
Email Address
INSTRUCTIONS FOR STUDENTS:
(1) There are 8 pages including this cover page and 5 formula sheets. Each of the five
numbered problems is
STAT 630Formulas for the Final Exam
Cumulative Distribution Function
The cdf of a random variable X is a function FX (x) = P (X x)
for each x.
Relationship of CDF and PDF for a Continuous RV fX (x) =
STATISTICS 630 - Final Exam
December 15, 2015
Name
Email Address
INSTRUCTIONS FOR STUDENTS:
(1) There are 8 pages including this cover page and 5 formula sheets. Each of the five
numbered problems is
STATISTICS 630 - Solution to Test II
November 9, 2016
1. Let Z1 , . . . , Z8 be independent standard normal random variables. Identify completely
the distribution including the parameters of each of t
STATISTICS 630 - Test II
November 6, 2013
Name
Email Address
INSTRUCTIONS FOR STUDENTS:
(1) There are seven pages including this cover page and four formula sheets. Each of the
five numbered problems
STATISTICS 630 - Test II
November 11, 2015
Name
Email Address
INSTRUCTIONS FOR STUDENTS:
(1) There are seven pages including this cover page and four formula sheets. Each of the
five numbered problems
STATISTICS 630 - Test II
November 9, 2016
Name
Email Address
INSTRUCTIONS FOR STUDENTS:
(1) There are seven pages including this cover page and four formula sheets. Each of the
four numbered problems
STATISTICS 630 - Solutions to Test II
November 6, 2013
1. Suppose that the random variables (X, Y ) have joint probability density function (pdf)
cfw_
15x2 y, 0 < x < y < 1,
f (x, y) =
0,
otherwise.
Y