# MATH 2030 3.0MW (Elementary Probability) Assignments - Winter 2011

Assignments and their solutions will be posted here as they become available.

### Practice problems

Not to be handed in.
• Section 3.1, numbers 2, 6 (and also find E[XY] and Var[XY])
• Section 6.4, numbers 1d, 5 (and also find the marginal distribution of Y)
• Choose a number X uniformly at random from the numbers 1, 2, 3. Given the value of X, choose a number uniformly at random from the numbers 1, ... , X; Find the joint distribution of (X,Y). Then find the marginal distributions of X and Y. Then find the correlation and covariance of X and Y.
Solutions

### Assignment 8

Due 5pm, Tuesday April 5, 2011
• Section 2.4, number 4
• Section 3.4, number 4
• Section 3.5, numbers 2, 8, 10ab, 11a
• Section 4.2, numbers 3bc, 4abc
Solutions
70 marks

### Assignment 7

Due 5pm, Monday March 28, 2011
• Section 3.3, numbers 2, 3, 8bc, 12, 14, 20
• Section 4.1, numbers 2c, 3e (variance only), 9
Solutions
Total: 30 marks.

### Assignment 6

Due 5pm, Friday March 11, 2011
• Section 3.2, numbers 5, 8, 13ad, 14
• Section 4.1, numbers 2b, 3e (mean only)
Solutions
All 6 questions were graded, for a total of 60 marks.

### Assignment 5

Due 5pm, Friday March 4, 2011
• Section 2.1, numbers 4, 7
• Section 2.2, numbers 4, 8, 9
Solutions
All 5 problems were graded, for a total of 10 marks.

### Assignment 4

NOW DUE MONDAY FEB 28, 5PM
(originally due Friday, February 18, 2011)
• Section 3.1, number 9
• Section 4.1, numbers 2a, 3abcd, 12a
• Section 4.4, number 10c (using cdf's: write the cdf of 1/Z as an integral using the density of Z, and then differentiate using the fundamental theorem of calculus)
• Review problems to Chapter 4, number 4c (find the cdf and then also the density)
• Section 4.5, numbers 2a, 5, 6ab
Solutions (corrected)
The 5 problems graded were 4.1 numbers 3, 12; 4.5 numbers 5, 6; Chapter 4 review problem 4, for a total of 25 marks.

### Assignment 3

due Friday, February 4, 2011 (in class, or by 5pm in the assignment box)
• Section 1.5, numbers 3, 6ac
• Section 1.6, numbers 1, 6, 7, 8
• The Monty Hall problem: You are playing a game show, in which there are prizes behind three doors. One prize is good (eg a car), and the others aren't (eg. a goat and a rabbit). Once you pick a door, the host (named Monty Hall) will open one of the other doors, showing you a bad prize. And he will ask you if you want to switch your choice. Should you?

The argument against is that since he always opens a door, he hasn't really given you any information that would favor one door over the other. So both remaining doors are equally likely to be correct (conditional prob 1/2 each), and there is no point in switching. The argument for switching is that you have no new information about your original choice. So the probability you picked correctly in the first place is unchanged at 1/3, and the (conditional) probability the other door is correct is now 2/3. Which argument is right?

Solutions (corrected)
Six problems were graded, for a total out of 60 marks. The only ungraded one was the Monty Hall problem.

### Assignment 2

due Friday, January 28, 2011 (in class, or by 5pm in the assignment box)
• Section 1.4, numbers 4, 5, 6, 7, 8
Solutions
All 5 problems were marked, giving a score out of 50.

### Assignment 1

due Friday, January 21, 2011 (in class, or by 5pm in the assignment box)
• Section 1.1, numbers 2, 7. In number 2, write down explicitly what Omega you are using, and what the event is (as a set) in each case.
• Section 1.3, numbers 2, 4, 5, 6, 9
• Appendix I, numbers vii, viii, x, xii, xiii
Solutions (corrected)
The 5 problems graded were 1.1 number 2, 1.3 numbers 4 and 6, Appendix numbers vii and xii, giving a score out of 10