BTRY/STSCI 4090: Homework 3
Due: In section, 12:20pm: Friday, March 28, 2013
Please show all work. A complete solution includes an explanation/derivation
as appropriate, not just an answer.
1
Free throws until rst in
You want to estimate the probability,

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BTRY 4090 / STSCI 4090
Spring 2011
Homework 2 Solutions
1. L&M p. 297, Question 5.2.16
2. L&M p. 297, (a) Question 5.2.20. (b) Find the maximum likelihood estimates for 1 and 2.
3. L&M p. 309, Question 5.3.2.
4. L&M p. 311, Question 5.3.22. Note: In (a),

BTRY 4090 / STSCI 4090
Spring 2011
Homework 6
Due at 2:00pm on Friday, March 18 in 1198 Comstock Hall
(Note: This assignment is about half the usual length, consisting of 6 questions)
1. We wish to test H0: p = 0.6 versus H1: p < 0.6 using binomial data w

BTRY 4090 / STSCI 4090
Spring 2011
Homework 8
Due at 2:00pm on Friday, April 8 in 1198 Comstock Hall
1. If the variances of two normal populations are unequal, the result can greatly affect the true
error rate of a test with nominal significance level 0.0

BTRY 4090 / STSCI 4090
Spring 2011
Homework 7
Due at 2:00pm on Friday, April 1 in 1198 Comstock Hall
1. We observe a random sample X 1 , X 2 ,., X n from the beta(,1) distribution and an
independent random sample Y1 , Y2 ,., Ym from the beta(,1) distribut

BTRY 4090 / STSCI 4090
Spring 2011
Homework 10
Due at 2:00pm on Friday, April 29 in 1198 Comstock Hall
1. Larsen & Marx p. 543, Questions 11.2.14 and 11.2.15.
2. Here are four regression data sets, with predictor xi and response yi for data set i = 1,2,3,

BTRY 4090 / STSCI 4090
Spring 2011
Homework 9
Due at 2:00pm on Friday, April 22 in 1198 Comstock Hall
1. Larsen & Marx p. 498, Question 10.2.4 modified:
(a) As stated in L&M.
(b) Find the probability that of 7 enlistees, at most 2 will belong to class I a

BTRY 4090 / STSCI 4090
Spring 2011
Homework 11
This assignment is half the usual length; it will be weighted accordingly
Due at 2:00pm on Friday, May 6 in 1198 Comstock Hall
1. Larsen & Marx pp. 554-555, Question 11.2.31. Note: Of course, you must find th

BTRY 4090 / STSCI 4090 Spring 201 1
Homework 4 Solutions
1. Larsen & Marx p. 333, Question 5.7.2.
Since 2 O, for each 1'. E (1?) z 02. By the weak law of large numbers demonstmted in Exempte
1 n 'J . . . 7 . . 3
5.7.2, E K as a eonsmtent esnmntor of the m

BTRY 4090 / STSCI 4090
Spring 2011
Homework 5
Due at 2:00pm on Friday, March 11 in 1198 Comstock Hall
1. Larsen & Marx p. 360, Question 6.2.1 modified: For each of the following hypothesis tests,
state the decision rule, evaluate the appropriate test stat

BTRY 4090 / STSCI 4090
Spring 2011
Homework 4 Notes
As with the earlier homeworks, the hard part of most questions is figuring out what to do. The
actual operations are usually pretty straightforward. Sometimes they involve cumbersome
expressions, for exa

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BTRY 4090 / STSCI 4090
Spring 2011
Homework 2
Due at 2:00pm on Friday, February 11 in 1198 Comstock Hall
Read Homework Policy and Instructions before you begin this assignment.
Use computer software of your choice for calculations too laborious to be feas

BTRY 4090 / STSCI 4090
Spring 2011
Homework 4
Due at 2:00pm on Friday, February 25 in 1198 Comstock Hall
1. Larsen & Marx p. 333, Question 5.7.2.
2. Larsen & Marx p. 333, Question 5.7.4.
3. Larsen & Marx p. 344, Question 5.8.2, modified as follows: Based

BTRY 4090 / STSCI 4090
Spring 2011
Homework 3
Due at 2:00pm on Friday, February 18 in 1198 Comstock Hall
Revised 2/17/11, 2:00pm: in Question 11, see correction of typo in subscripts; revised versions
are indicated by [T], and new text is in boldface.
1.

BTRY 4090 / STSCI 4090
Spring 2011
Homework 1
Due at 2:00pm on Friday, February 4 in 1198 Comstock Hall
Read Homework Policy and Instructions before you begin this assignment.
Use computer software of your choice for calculations too laborious to be feasi

BTRY/STSCI 4090
Section 7
Priors that are not conjugate for a likelihood
We have seen, so far, that posteriors often ends up in the same family as the prior. This is
in general not the case, and is the exception rather than the rule. This happened because

BTRY/STSCI 4090: Homework 5
Due: Wednesday, 5/7, 1:30pm, at Comstock 1198 (Beatrix Johnsons desk).
Please show all work. A complete solution includes an explanation/derivation as appropriate,
not just an answer.
1
Delta Method
Suppose X1 , . . . , Xn are

BTRY/STSCI 4090
Section 1
Linearity of the expected value and homogeneity of the
variance
The expected value is linear, in the sense that for any two random variables, E[X + Y ] =
E[X] + E[Y ], and for any constant c, E[cX] = c E[X]. To see this, consider

BTRY/STSCI 4090
Section 2
Sum of Independent Poissons
Let us prove the following nice property of the Poisson distribution. Say we have X1 , ., Xn
independent random variables with distributions Xi Poisson(i ). Then X1 + . + Xn
Poisson(1 + . + n ).
To se

HW 1 Bonus Part C
Ziyad Knio
February 10, 2014
> n = 10
> a = 0.05
> mu = 0
>
> nsim = 10000
>
> X = rep(NA, nsim)
>
> for(i in 1:nsim)
+cfw_
+
X[i] = mean(rnorm(n, mean=mu, sd=1)
+
>
> k = qnorm(2-a)/2)
>
> L = mu - k/sqrt(n); L
[1] -0.619795
> U = mu +

BTRY/STSCI 4090 Syllabus
Professor:
TA:
Jacob Bien
1178 Comstock Hall
Didier Chtelat
e
1187 Comstock Hall
(jbien@cornell.edu)
Oce hours: Tues 11:30am12:30pm or by appointment
(dc623@cornell.edu)
Oce hours: Mon 12:00pm1:00pm, Fri 1:15pm2:15pm
Website: See

BTRY/STSCI 4090: Homework 4
Due: In class, 10:10am: Tuesday, April 15.
Please show all work. A complete solution includes an explanation/derivation as appropriate,
not just an answer.
1
Suciency for sample of Poisson random variables
Suppose X1 , . . . ,