INTRODUCTION TO PROBABILITY AND STATISTICS II
Assignment #9 Solutions
36-226
Spring, 2009
Problem #1
x475
The test statistics for testing H0 : = 475 versus Ha : > 475 is z = 100/n . We will use the p-value
that corresponds to each test to determine whethe
INTRODUCTION TO PROBABILITY AND STATISTICS II
36-226
Assignment #7
Spring, 2009
NOTE: Be sure to write your name and staple your pages together. Numerical answers alone will not receive full credit. Be sure to show your work. Exam II, Wednesday, April 1,
36-226 INTRODUCTION TO PROBABILITY & STATISTICS II
SPRING 2010
MIDTERM II - April 5th 2010 7pm - 9pm
You must show your work and/or explain your steps in order to get full credit or be considered
for partial credit.
This is a closed book/closed notes exam
INTRODUCTION TO PROBABILITY AND STATISTICS II
36-226
Assignment #9
Spring, 2009
Due: Wednesday, April 15, at the beginning of class.
NOTE: Be sure to write your name and staple your pages together. Numerical answers alone will not receive
full credit. Be
INTRODUCTION TO PROBABILITY AND STATISTICS II
36-226
Assignment #6
Spring, 2009
Due: Wednesday, March 4 at the beginning of class.
NOTE: Be sure to write your name and staple your pages together. Numerical answers alone will not receive full credit. Be su
36-226 INTRO TO PROBABILITY & STATISTICS II N08
PRACTICE MIDTERM
You must show your work and/or explain your steps in order to get full credit or be considered for
partial credit.
This is a closed book/closed notes exam. You may use a onesided sheet of no
INTRODUCTION TO PROBABILITY AND STATISTICS II
36-226
Assignment #5
Spring, 2009
Due: Wednesday, February 25 at the beginning of class. NOTE: Be sure to write your name and staple your pages together. Numerical answers alone will not receive full credit. B
INTRODUCTION TO PROBABILITY AND STATISTICS II
36-226
Assignment #2
Spring, 2009
Due: Wednesday, January 28 at the beginning of class. NOTE: Be sure to write your name and staple your pages together. Numerical answers alone will not receive full credit. Be
INTRODUCTION TO PROBABILITY AND STATISTICS II
36-226
Assignment #8
Spring, 2009
Due: Wednesday, April 8, at the beginning of class.
NOTE: Be sure to write your name and staple your pages together. Numerical answers alone will not receive
full credit. Be s
INTRODUCTION TO PROBABILITY AND STATISTICS II
Assignment #3
36-226
Spring, 2009
Due: Wednesday, February 4 at the beginning of class.
NOTE: Be sure to write your name and staple your pages together. Numerical answers alone will not receive
full credit. Be
INTRODUCTION TO PROBABILITY AND STATISTICS II
Assignment #8 Solutions
36-226
Spring, 2009
Problem #1
(a) H0 : = 18 vs H0 : < 18;
(b) H0 : = 50 vs H0 : > 50;
(c) H0 : = 24 vs H0 : = 24;
Problem #2 The test statistic Y has a binomial distribution with n = 2
INTRODUCTION TO PROBABILITY AND STATISTICS II
36-226
Assignment #7 Solutions
Spring, 2009
Problem #1
Part I.
The investigators are interested in whether seeding clouds with silver iodide increases the amount of rain
produced by the cloud. Clouds were rand
INTRODUCTION TO PROBABILITY AND STATISTICS II
Assignment #6 Solutions
36-226
Spring, 2009
Problem 2
1
(a) L( ) = 2n (x1 xn )e
n
i=1
n
n
i=1
1
= 2n e
xi
xi
xi , )h(x1 , . . . , xn )
(x1 xn ) = g (
i=1
where h(x1 , . . . , xn ) = x1 x2 xn . A sufcient sta
INTRODUCTION TO PROBABILITY AND STATISTICS II
Assignment #5 Solutions
36-226
Spring, 2009
Problem #1
(a) The following is the MINITAB output for the condence interval:
Difference = mu (A) - mu (B)
Estimate for difference: -0.408
95% CI for difference: (-0
INTRODUCTION TO PROBABILITY AND STATISTICS II
Assignment #4 Solutions
36-226
Spring, 2009
Problem #1
(a) From the useful fact we have E ( n ) = n or n E ( ) = n E ( ) =
(b) Note: V ar ( n ) =
n2
V ar () = 2n. Therefore, V ar () =
(c) lnf (y | ) = 1 ln(2 )
INTRODUCTION TO PROBABILITY AND STATISTICS II
Assignment #3 Solutions
36-226
Spring, 2009
Problem #1
(a) Let T =
Z
W
, where Z Normal(0, 1) and W Chi-square ( ). The moment generating function of
Z is MZ (t) = et /2 Using the moment-generating function ap
Figure 1: Box Plots for WASTAGE in Mill A compared to Mill B
INTRODUCTION TO PROBABILITY AND STATISTICS II
36-226
Assignment #2 Solutions
Spring, 2009
Problem #1
The Levi-Strauss company is interested in two questions related to quality control at two mil
36-226 INTRODUCTION TO PROBABILITY & STATISTICS II
SPRING 2010
MIDTERM 1 - FEBRUARY 16th 2010
You must show your work and/or explain your steps in order to get full credit or be considered for
partial credit.
This is a closed book/closed notes exam. You m
36-226 INTRODUCTION TO PROBABILITY & STATISTICS II
SPRING 2010
PRACTICE - MIDTERM II
You must show your work and/or explain your steps in order to get full credit or be considered for
partial credit.
This is a closed book/closed notes exam. You may use a
36-226 HOMEWORK 2
Due: Friday 1/30/15 at 9:30am in class
Remember to show all work; just writing down the answer will not receive credit.
x
1. Let X Exp(2), i.e. fX (x) = 1 e 2 where 0 < x < .
2
(a) Use the Method of Distribution Functions to nd the distr