Assignments - Fall 2008

- Section 2.4, numbers 4, 5
- Section 2.5, number 9b
- Section 3.1, number 15
- Section 3.3, numbers 3, 12, 17
- Section 3.4, numbers 2, 4, 12ad
- Section 3.5, numbers 4, 6, 10ab, 11
- Section 4.1, number 9
- Section 4.2, numbers 1, 3bc, 4abc

- Section 3.2, numbers 8, 14
- Section 3.3, numbers 2, 5, 8bc
- Section 4.1, numbers 2bc, 3e

- Section 2.1, number 6
- Section 2.2, numbers 8, 9
- Section 4.4, numbers 4, 10a.

In 4 I want you to compute the cdf first, and then the density. In 10a I want you to relate the cdf to the standard normal cdf, and then take derivatives.

- Section 1.5, numbers 3, 6ac
- 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 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 favour 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 is right?

- Section 4.1, numbers 3ab, 4a, 12a
- Section 4.5, numbers 2a, 5, 6ab

- Section 1.4, numbers 4, 5, 6, 7, 8
- Section 1.6, numbers 4, 6, 7, 8

- Section 1.1, numbers 3, 7
- Section 1.3, numbers 2, 4, 5, 6, 9
- Appendix I, numbers vii, viii, x, xii, xiii