There will be homeworks collected weekly and one midterm.
The final grade will be weighted as follows:
Homework 30%, midterm 25%, final 45%.
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.