### Math 1620: Statistics

####
Professor Richard Kenyon

Tel. 863-6406

rkenyon -at- math dot brown dot edu

office: Kassar 305

Office hours: M 1-3pm, Thurs 3-4pm

**Text:** Statistics, 4th ed. Freedman, Pisani, Purves

There will be homeworks collected weekly and one midterm.

The final grade will be weighted as follows:
Homework 30%, midterm 25%, final 45%.

#
final: May 6, 9am, Barus-Holley 141. (Note room change!)

You may bring one page of notes and a calculator.

midterm: March 10 in class

Late homework will not be accepted.

Your lowest homework grade will be dropped.

** Homework 1 due Tues Feb 3 in class: **

Page 24, Review exercises, 1-12.

Page 50ff: 6,7,10,11,12

** Homework 2 due Tues Feb 10 in class: **

Page 94: 3

Page 106: 7,13

Page 137: 9a, 12

Page 154: 4,7,9,10

** Homework 3 due Thurs Feb 19 in class: **

Page 176: 4,5,8

Page 198: 3,4,7,11

Page 214: 2,5,7,9,12

Extra problem: n fair dice are rolled. Compute the correlation
coefficient between the sum of the first k and the sum of the last k,
for all k from 1 to n.

** Homework 4 due Thurs Feb 26 in class: **

Page 154: 4 (assume there are 500 men and 500 women; compute the correlation
explicitly).

Page 215: 10

Page 286: 9

Page 329: 15

X1. (X,Y) is a joint Gaussian RV with density proportional to exp(-2x^2-xy-4y^2).
Compute the covariance matrix. What is the correlation between X and Y?

X2. Class grades on three tests X,Y,Z
each average 60 with SD=15. The correlations
between the grades are r(X,Y)=.6, r(X,Z)=.7, r(Y,Z)=.8;
given that a student scores 75 on tests X and Y,
what is his expected score on Z?

X3. In the previous problem, suppose we don't know r(Y,Z). Can
Y and Z be negatively correlated?

X4. 100 independent draws from an exponential RV are given. Is the correlation
between the largest and second largest going to be positive, zero, or negative?

** Homework 5 due Thurs March 12 in class: **

Page 352: 5,6,7,12

Page 372: 5,6,8

Page 391: 2,3,7,9,14

Page 406:3,6

** Homework 6 due Thurs March 19 in class: **

Page 426: 2,3,4

Page 432: 20

Page 436: 24,28

** Homework 7 due Tues April 7 in class: **

Homework 7

** Homework 8 due Tues April 14 in class: **

Homework 8

** Homework 9 due Tues April 21 in class: **

Homework 9

** Reading:**

For Jan 27: Read Chapters 1,2,3,4 (pp 1-76).

For Feb 5: Read Chapters 8-10.

For Feb 12: Read Chapters 11-12.

For Feb 24: Read Chapters 19-20.

For Mar 3: Read Chapters 21-23.