36-226 INTRODUCTION TO PROBABILITY & STATISTICS II 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/c
STAT 226 - HW 9
Due Monday April 24
Do the following problems 1. Let X1 , X2 , . . . , Xn be a random sample from a N (, 2 ) distribution, where 2 is known. The following two simple hypotheses are bei
STAT 226 - Solutions to Homework 7
Problem 1 (9 points: (a) 4 (b) 2 (c) 3)
(a) A 100(1 )% CI for ( is known) is X z/2 . In this case, a 95% C.I. for
n
, the mean ARSMA score of the rst generation Mexi
STAT 226 - Homework 8
Due Monday April 10
instructions:
1. This homework is due Monday , April 10 in class, BEFORE class starts. No HW
will be accepted after the assignments have been collected.
2. Pl
STAT 226 - Solutions to Homework 8
Problem 1
X1 , X2 , ., Xn iid exp( ).
(a)
1
L( ) = ( )n e1/
n
i=1
1
ln L( ) = n ln
ln L( )
n
1
= + 2
xi
n
xi
i=1
n
xi = 0
i=1
n
n +
=
xi = 0
i=1
n
i=1
2 ln L( )
n
STAT 226 - Homework 7
Due Friday March 31
Do the following problems:
1. The Acculturation Rating Scale for Mexican Americans (ARSMA) is a psychological test developed to measure the degree of Mexican/
STAT 226 - Solutions to Homework 4
Problem 1 (20 points: (a) 10 [2 for each expected value] (b) 20 points [2
for each variance, 2 for identifying the one with smallest variance)
Recall that if X exp(
STAT 226 - Solutions to Homework 5
Problem 1
1
n
n n
xi
L( ) = 2
i=1
using the factorization theorem:
h(X1 , ., Xn ) = [
n
i=1
xi ]
g (, T ) = n 2n [
n
i=1
xi ]
1
T =
n
i=1
xi is sucient for
Probl
STAT 226 - Homework 5 - Suciency and MVUE
Due Friday February 24 -BEFORE CLASS STARTS
Do the following problems:
1. Let X1 , X2 , . . . , Xn be a random sample from the following distribution:
2
x>2
STAT 226 - Homework 6
Due Friday March 24, before class starts
Topics Covered by this HW assignment:
(i) Bayesian Estimation
(ii) Distributions Derived from the Normal Distribution.
I. Read sections 7
STAT 226 - Solutions to Homework 3
Problem 1
(14 points: (a) 8 [3 for L(), 3 for ciritical point, 2 for max] (b) 2 (c) 4 [-2 if no
explanation])
a)
n
n
e xi
en i=1 xi
=
L() =
n
xi !
i=1 xi !
i=1
n
n
l
36-226 - Solutions to HW 2
Problem 1 15 points: (a) 6 points [3 for E(X), 3 for (V(X)] (b) 5 points (0 if
E(1/X) = 1/E(X), (c) 4 points
a) Recall that if X exp( ) then, E (X ) = and V (X ) = 2 . There
STAT 226 - Homework 4 - Properties of Estimators
Due Friday February 17 -BEFORE CLASS STARTS
I. Read sections 9.4, 8.5, 8.6
II. Do the following problems:
1. Page 368, problem 8.4
Note: It be useful t
STAT 226 - Homework 3 - M.L.E
Due Friday February 10 -BEFORE CLASS STARTS
I. Read sections 8.2, 8.3, 9.2 (if you havent done so already) and 9.4
II. Do the following problems:
1. Page 453 problems 9.7
36-226 Handout for Lecture # 1
January 16, 2006
Example 1:
The following data are the weight of 125 newborns.
3870
3200
2950
2520
2780
2460
3300
3520
2850
2870
2620
4010
3400
3100
2800
3670
2860
3300
STAT 226 - Homework 2
Due Friday February 3 - BEFORE CLASS STARTS
Topics covered in this assignment:
Examining properties of sample statistics (by reviewing 36-225 material)
Joint density of a rando
STAT 226 - Homework 1 - Exploratory Data Analysis
You can learn a lot just from looking at the data!
Due Friday January 27 - Before class starts
Comments:
1. This assignment requires the use of the st