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== Problem 2: A Bayesian Proof == | == Problem 2: A Bayesian Proof == | ||
| + | The theorem of total probability states that <math>P(A) = P(A|C)P(C) + P(A|C^c)P(C^c)</math>. Show that this result still holds when everything is conditioned on event $B$, that is, prove that | ||
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| + | <math>P(A|B) = P(A|B\cap C)P(C|B) + P(A|B\cap C^c)P(C^c|B).</math> | ||
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[[HW3.2 - Steve Anderson_ECE302Fall2008sanghavi]] | [[HW3.2 - Steve Anderson_ECE302Fall2008sanghavi]] | ||
Revision as of 07:09, 18 September 2008
Contents
Instructions
Homework 3 can be downloaded here on the ECE 302 course website.
Problem 1: Monte Hall, twisted
http://nostalgia.wikipedia.org/wiki/Monty_Hall_problem Explains the original Monty Hall problem and then the problem considering two contestants are involved.
Consider the following twist on the monty hall problem (see video above to recollect):
There are 3 doors, behind one of which there is a car, and the remaining two have goats. You and a friend each pick a door. One of you will have definitely picked a goat. The host then opens one of the two chosen doors (i.e. yours or your friend's), shows a goat and kicks that person out (if both of you have chosen goats, he opens one door at random). The other person is given the option of staying put, or switching to the one remaining door.
- (a) When originally picking your doors, should you choose your door first, or let your friend go first? Does it make a difference?
HW3.1.a Zhongtian Wang_ECE302Fall2008sanghavi
HW3.1.a Shao-Fu Shih_ECE302Fall2008sanghavi
HW3.1.a Beau "ballah-fo-life" Morrison_ECE302Fall2008sanghavi
HW3.1.a Suan-Aik Yeo_ECE302Fall2008sanghavi
HW3.1.a Chris Wacnik_ECE302Fall2008sanghavi
HW3.1.a Chris Cadwallader_ECE302Fall2008sanghavi
HW3.1.a Dan Van Cleve_ECE302Fall2008sanghavi
HW3.1.a Joe Gutierrez_ECE302Fall2008sanghavi
- (b) It turns out that the host has just eliminated your friend. What should you do? (i.e. stick with your original door, or switch?) What are the probabilities of winning in each case?
HW3.1.b Zhongtian Wang & Jonathan Morales_ECE302Fall2008sanghavi
HW 3.1b Albert Lai_ECE302Fall2008sanghavi
HW3.1.b Spencer Mitchell_ECE302Fall2008sanghavi
HW 3.1b Sahil Khosla_ECE302Fall2008sanghavi
HW 3.1b Virgil Hsieh_ECE302Fall2008sanghavi
HW 3.1b Ben Wurtz_ECE302Fall2008sanghavi
HW 3.1b Vivek Ravi_ECE302Fall2008sanghavi
HW3.1.b Anand Gautam_ECE302Fall2008sanghavi
HW3.1.b Steve Streeter_ECE302Fall2008sanghavi
HW3.1.b Kushagra Kapoor_ECE302Fall2008sanghavi
HW3.1.b Anthony O'Brien_ECE302Fall2008sanghavi
HW3.1.b Seraj Dosenbach_ECE302Fall2008sanghavi
HW3.1b Priyanka Savkar_ECE302Fall2008sanghavi
HW3.1.b Emily Blount_ECE302Fall2008sanghavi
Problem 2: A Bayesian Proof
The theorem of total probability states that $ P(A) = P(A|C)P(C) + P(A|C^c)P(C^c) $. Show that this result still holds when everything is conditioned on event $B$, that is, prove that
$ P(A|B) = P(A|B\cap C)P(C|B) + P(A|B\cap C^c)P(C^c|B). $
HW3.2 - Steve Anderson_ECE302Fall2008sanghavi
HW3.2 Tiffany Sukwanto_ECE302Fall2008sanghavi
HW3.2 Sang Mo Je_ECE302Fall2008sanghavi
HW3.2 Emir Kavurmacioglu_ECE302Fall2008sanghavi
HW3.2 Phil Cannon_ECE302Fall2008sanghavi
HW3.2 Sourabh Ranka_ECE302Fall2008sanghavi
Problem 3: Internet Outage
HW3.3 Gregory Pajot_ECE302Fall2008sanghavi
HW3.3 Monsu Mathew_ECE302Fall2008sanghavi
HW3.3 Joe Romine_ECE302Fall2008sanghavi
HW3.3 Katie Pekkarinen_ECE302Fall2008sanghavi
HW3.3 Jayanth Athreya_ECE302Fall2008sanghavi
HW3.3 Steven Millies_ECE302Fall2008sanghavi
HW3.3 Carlos Leon_ECE302Fall2008sanghavi
Problem 4: Colored Die
HW3.4.a Seraj Dosenbach_ECE302Fall2008sanghavi
HW3.4.a Shweta Saxena_ECE302Fall2008sanghavi
HW3.4.a Joshua Long_ECE302Fall2008sanghavi
HW3.4.a Eric Zarowny_ECE302Fall2008sanghavi
HW3.4.a Anand Gautam_ECE302Fall2008sanghavi
HW3.4.b Joon Young Kim_ECE302Fall2008sanghavi
HW3.4.b Jared McNealis_ECE302Fall2008sanghavi
HW3.4.b Seraj Dosenbach_ECE302Fall2008sanghavi
HW 3.4.c Junzhe Geng_ECE302Fall2008sanghavi
HW3.4 Aishwar Sabesan _ECE302Fall2008sanghavi
HW3.4c AJ Hartnett_ECE302Fall2008sanghavi
HW3.4a Jaewoo Choi_ECE302Fall2008sanghavi
HW3.4c Patrick M. Avery Jr._ECE302Fall2008sanghavi
Problem 5: Fuzzy Logic
3.5 - Nicholas Browdues_ECE302Fall2008sanghavi
3.5 - Divyanshu Kamboj_ECE302Fall2008sanghavi
3.5 - Katie Pekkarinen_ECE302Fall2008sanghavi
3.5 - Caleb Ayew-ew_ECE302Fall2008sanghavi
3.5 - Brian Thomas_ECE302Fall2008sanghavi
3.5 - Justin Mauck_ECE302Fall2008sanghavi
