### 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
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