| Chapter |
Essential Problems |
| 1.3 |
#5, #7, #9, #11, #13 Extra Problem: Use the axioms of probability to prove the formulas given for P(A) when the sample space S is finite and all outcomes are equally likely. Extra Problem (HARD): Consider the discrete set { 1/N, 2/N, .... ,1 } (N is any fixed positive integer). Pick an outcome uniformly at random from this set. For any interval A contained in [0,1], compute the probability that the outcome is in A. For A fixed, consider the value of P(A) as N tends to infinity. Identify the limiting value, which we denote by P(A). Show that P(A) satisfies the axioms for a probability as we have defined them in 1.3 with respect to sets A which are mutually disjoint finite unions of subintervals of [0,1]. (In particular, verify the additivity axiom). Can you identify P(A) with any distribution that has been defined thus far? |
| 1.4A |
#2, #6, #8, #12 |
| 1.3 and 1.4A Due Week 2 |
|
| 1.4B |
#4, #10 The Monty Hall Problem: The Gameshow `Lets make a deal' was popular back in the 70's. In it a contestant was asked to select one of three doors. behind each door was a `prize'; Two legit and one a dud (say a years supply of dog food....). After the selection is made by a contestant, Monty Hall (the host) reveals what was behind one of the remaining doors (not selected by contestant). Always he revelas a door which contains a legit prize. Then, he asks the contestant if they would like to switch their selection to the other remaining door. What should the contestant do? Is there a strategy which maximizes the frequency with which he or she wins? Hint: Try and compute conditional probabilites of winning depending on where the dud prize is. Hint 2: THIS IS A FAMOUS PROBLEM. You could (if you are really stuck) find it online. |
| 1.5 |
2, 7, 8 |
| 1.6 |
2, 4 |
| 1.4B, 1.5, 1.6a Due Week 3 |
|
| 1.6b |
6, 7, 8 For each k, give an example of a proability space and events A_1,..., A_k on the space so that A: each k-1 grouping is independent B: The entire collection is not Hint: Try to generalize our 2 coin example for k=3 |
| 2.1 |
2, 6, 8, 10, 14 |
| 1.6b, 2.1 due Week 4 |
|
| 2.2a |
1, 6, 9, 12, .... 15 (for some
calculus practice....) |
| 2.2b |
16, 17 |
| 2.4 |
2, 4, 6, 8 |
| 2.2ab , 2.4 due Week 5 |
|
| 2.5 |
Evens |
| Due by Teusday at Exam. |
|
| 3.1 |
4, 5, 10, 17, 20, 22 |
| 3.2 |
10, 14, 16, 20 |
| Due Thurs. March 6 |
|
| 3.3 |
3, 8, 10, 16, 18, 22, 26, 30 |
| Due Thurs. March 13 |
|
| 3.4 |
All Even Problems |
| Due Thurs. March 20 |
|
| 3.5 |
4, 8, 11, 14, 17, 18 |
| Ch 3 Review (for practice only) |
Warmup: 4, 6, 9, 14, 16, 21 Serious: 22, 24, 29, 30, 33 Hard: 31 Hardest: 41 |
| 4.1 |
2, 3, 4, 7, 10, 11 |
| 3.5, 4.1 due April 8 |
|
| 4.2 |
4, 6, 8, 12, 13 |
| 4.2 due April 10 |
|
| 4.4 |
1, 2, 4, 6, 10 |
| 4.5 |
4, 5, 6, 8 |
| 4.6 |
No Longer part of HW |
| 4.4, 4.5 due day of
midterm (in principle you may hand them in on thurday April 17 BUT they
will be on the exam) |
|
| 5.1 |
1, 2, 4, 7, 8 |
| 5.2a |
2, 6, 11, 13 |
| Due April 24 |
|
| 5.3 |
2, 3, 4, 6, 8, 11 |
| Due May 1 |
|
| 6.1 |
4, 8 |
| 6.2 |
2, 4, 6, 7, 8, 17 |
| Due May 8 |
|
| 6.3 |
2, 4, 8, 10 |
| Due at Final Exam |