SOLUTIONS 2007
STA261
( c David Brenner, 2007, 2010) revised Mar. 8, 2010
1
2
3
4
5
7
8
9
10
total/70
UNIVERSITY OF TORONTO Faculty of Arts & Science APRIL-MAY EXAMINATIONS 2007
STA 261H1 S
Prof. D. Brenner Duration 3 hours
Examination Aids:
Non-programma
STA261 Assignment I
How dyuh like them apples!?
due: Wed.Feb.24/10
Understanding the relationship between one experimental variable and another is often the main objective of a given study. Simply plotting a sample of the joint outcomes for such variables
1
2
3
4
5
7
8
9
10
total/70
UNIVERSITY OF TORONTO Faculty of Arts & Science APRIL-MAY EXAMINATIONS 2007
STA 261H1 S
Prof. D. Brenner Duration 3 hours
Examination Aids:
Non-programmable Calculators
Instructions Please show all your work clearly in the spac
TEST 2
STA261
( c David Brenner, 2010) Mar.24, 2010
name
SOLUTIONS
student number
TA
(1)
Q1
Q2
Q3
Q4
total
Instructions: No aids are allowed other than non-programmable calculators. Please show all your work clearly in the space provided to obtain partial
STA261H1S
Questions and Solutions for Tutorial 7
Due: 6:00 pm July 25, 2016
Question 1 (Neyman-Pearson Lemma. Adapted from Chapter 9 Q18).
Let 1 , , be iid random variables from an Exp() distribution with density
1
() =
2
(a) Derive a likelihood ratio te
1
2
3
4
5
7
8
9
10
total/70
UNIVERSITY OF TORONTO Faculty of Arts & Science APRIL-MAY EXAMINATIONS 2008
STA 261H1 S
Prof. D. Brenner Duration 3 hours
Examination Aids:
Non-programmable Calculators
Instructions Please show all your work clearly in the spac
STA261H1S
Questions and Solutions for Tutorial 3
Due: 6:00 pm July 6, 2016
Question 1.
Suppose that 1 , , are iid random variables from a population with E[] = and Var[] = 2 . Show that
2 =
is a consistent estimator for 2 .
1
( )2
=1
Solution: Hint
1
1
STA261H1S
Questions and Solutions for Tutorial 6
Due: 6:00 pm July 20, 2016
Question 1 (Rao-Blackwell Theorem).
Suppose that 1 , , are iid random variables from Pois(). Let = =1 and 1 = 1
=1 . In tutorial
5, we have shown that is a sufficient statistic fo
University of Toronto
Faculty of Arts and Science
JUNE 2016 EXAMINATIONS
STA261H1S
Solutions
Duration 2 hours
(6:00PM - 8:00PM Wednesday, July 13, 2016)
Examination Aid: Nonprogrammable calculator (Statistical or programmable calculator is
NOT allowed)
La
STA261H1S
Questions and Solutions for Tutorial 3
Due: 6:00 pm July 11, 2016
Question 1 (Chapter8 Q6)
Suppose that ~Bin(, ) where p is unknown.
(a) Show that the MLE of p is =
(b) Show that is a consistent estimator for p
(c) Find the Fisher information I
STA261H1S
Questions and Solutions for Tutorial 1
Due: 6:00 pm June 29, 2016
Question 1. (Chapter 10 Q3)
From Figure 10.1, roughly what are the upper and lower quartiles and the median of the distribution of melting
points?
Solution:
Question 2 (Chapter 10
STA261H1S
Questions and Solutions for Tutorial 8
Due: 6:00 pm July 27, 2016
Question 1 (The generalized LR test and Chi-square goodness-of-fit tests. Chapter 9 Q37)
The following table gives the number of deaths due to accidental falls for each month duri
STA261 Assignment 2
due: Wed.Mar.31/10
A sequence of statistical estimates n with n N is said to be consistent for d the parameter i n as n . And any particular estimate T is said to be unbiased for i ET = . Thus, unbiasedness is about individual estimato
ESP I EXAMPLES FOR STUDY AND PRACTICE I
1. Suppose we have obtained the following sample of 10 outcomes from a the continuous uniform distribution U ! unif[0,1]
$1$ !STA261H"
U : .189, .841, .994, .777, .281, .008, .310, .098, .892, .620, . a) What is the
1
2
3
4
5
7
8
9
10
total/70
UNIVERSITY OF TORONTO Faculty of Arts & Science APRIL-MAY EXAMINATIONS 2008
STA 261H1 S
Prof. D. Brenner Duration 3 hours
Examination Aids:
Non-programmable Calculators
Instructions Please show all your work clearly in the spac
Last Name: First Name: Student #:
UNIVERSITY OF TORONTO
Faculty of Arts and Science Slo L UT] 0 K) S _
STA261HIS WINTER 2016 MIDTERM TEST
Duration110 minutes
Aid allowed: A non-programmable calculator
Aid provided: Statistical tables, Summary sheet
Instru