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--- spcs:summer2014:day_10 [2014/07/04 08:35]
ffpaladin [SPCS - Day 10]
+++ spcs:summer2014:day_10 [2015/07/05 16:35]
ffpaladin [Assignment]
@@ Line 1: / Line 1: @@
+====== SPCS - Day 10 ======
+Free Seating Friday!
+Afternoon Groups: Work individually or with a group if you'd prefer, but please ask for help, if you need it. Please help each other out!
+I'm doing one-on-one meetings with each of you on Monday!
+===== Topics =====
+  * Monty Hall
+  * Bayes
+  * https://www.youtube.com/watch?v=TYIh4MkcfJA
+  * Arduino
+  * https://www.youtube.com/watch?v=UoBUXOOdLXY
+  * Boolean Algebra
+  * Logic Gates: https://dl.dropboxusercontent.com/u/3235343/Teaching/Logicly.swf
+  * http://www.skot9000.com/ttl/datasheets/8.pdf
+  * http://www.skot9000.com/ttl/
+  * http://www.ee.calpoly.edu/media/uploads/resources/KarnaughExplorer_1.html
+  * Circuits
+  * https://www.khanacademy.org/science/physics/electricity-and-magnetism/v/circuits--part-1
+  * http://dlnmh9ip6v2uc.cloudfront.net/datasheets/Kits/SFE03-0012-SIK.Guide-300dpi-01.pdf
+===== Assignment =====
+Math Probability Problem (Optional Challenge)
+There is an urn containing three balls. Each ball is either red or blue, and two balls have the same color. So, there are two possibities: either two balls are red and one is blue (the “majority-red case”) or two balls are blue and one is red (the “majority-blue” case). The probability of both cases is the same, i.e., 50%.
+John is allowed to draw a random ball from the urn, look at it, and put it back. Then, he has to make a guess as to whether he thinks the urn is majority-blue or majority-red. Let’s say that John has drawn a red ball. It seems
+natural that John should guess that the urn is probably majority-red. We now ask you to confirm this is a good
+guess, using Bayes’ rule.
+Let “MajRed” be the event that the urn is majority-red. So, “not MajRed” is the event that the urn is not majorityred, which means that the urn is majority-blue. Let “RedBall” be the event that John picked a red ball. We are interested in the probability P(MajRed|RedBall) that the urn is majority-red given that John has picked a red ball.
+  * (a) What is the prior probability P(MajRed) according to the above description?
+  * (b) What is the conditional probability P(RedBall | MajRed)?
+  * (c) What is the conditional probability P(RedBall | not MajRed)?
+  * (d) Finally, using Bayes’ rule and other rules, what is the conditional probability P(MajRed | RedBall)?
+John decided to declare that he thinks the urn is majority-red. Next, it’s Mary’s turn to pick a random ball from the rn, look at it, and put it back. She picks a blue ball. Now, she is in the same situation as John: she has to make a guess about the urn based on what she has seen. But, she also knows that John has seen a red ball (because otherwise he would not have said that he thinks the urn is majority red).
+Mary is not sure what to think. On the one hand, she saw a blue ball, and therefore the urn is most likely majorityblue. On the other hand, she knows that John has picked a red ball, which suggests that the urn is majority-red.
+We can solve this problem again using Bayes’ rule. Let “RedThenBlue” be the event that John picked a red ball,
+and then Mary picked a blue ball (which is what happened).
+  * (e) What is the conditional probability P(MajRed | RedThenBlue)?
+Hint: this can be computed using the same techniques as in (a)-(d).
+Answer: http://users.soe.ucsc.edu/~sherol/teaching/doku.php?id=epgy:ai13:bayes_problem_solution
+===== Blog =====
+    * Projects (as usual)
+===== Arduino =====
+    * You know what to do!
+    * Take pictures and blog it!
+Have fun! Great work, class!
+===== Feedback =====
+https://docs.google.com/forms/d/1nNvgtxwBtGiDMfe_jjx1PH8MzwJlOR7jIAaEdLZ-sZI/viewform

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