This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
spcs:summer2014:day_10 [2014/07/03 21:50] ffpaladin [Assignment] |
spcs:summer2014:day_10 [2014/07/07 15:47] 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 |