Class Notes (834,037)
Canada (508,290)
Statistics (281)
STAB22H3 (223)
Ken Butler (34)
Lecture 10

STAB22-LEC10-(11)-MID.docx

10 Pages
56 Views
Unlock Document

Department
Statistics
Course
STAB22H3
Professor
Ken Butler
Semester
Fall

Description
STAB22 LEC10 NOTE: This lecture ONLY lasted till 34:12; it finishes up Chapter 11 Some notes about changes to his webpage (see the page here: http://utsc.utoronto.ca/~butler/b22 - About EXAM - from C1 to C11 - CONTENT EXEMPTED FROM EXAM? - timeplots - Plan B: Attack of the Logarithsm - do not have to calculate a correlation by hand TA OFFICE HOURS - IC404 (check the timings for Fri, Mon) WHEN IS THE EXAM? - Exam at Mon; 5-7pm ----------------------------- CHAPTER 11 - UNDERSTANDING RANDOMNESS [128] - The following games are random - tossing a coin - rolling a 6-sided dice - For sth to be random, it is - unexpected (unpredictable) in the short-term, but is - predictable in the long-term (ie. if you do trials over and over again, what will your likelihood be of getting X?) (ex) that shows that randomizations are predictable in the long-term: a) coin: - should get heads or tails about 1/2 of the time b) die - should roll a certain number from 1 to 6 about 1/6 of the time (ex) take randomizing device (ex. dice); if they are rolled, do not know what exactly will come up in the next roll (ie. in the short-term), but will know what will likely turn up to be in the long-term Computer random numbers - they are gen'ed by a computer algorithm - aka pseudorandom numbers, b/c they are prod'ed by a non-random method => the computer can make the #'s look like as if they are random, even tho. they are entirely prod'ed by a nonrandom method [129] RANDOM DIGIT TABLES What is a simulation? - It is sth that models that real-world scenario by using random-digit outcomes to imitate the uncertainty of a response var. of interest - ie. they are copying the probability of a certain val. of the response var. to appear, but depicting so with random numbers - can do simulation easily via a computer (ie. get a statistics package to list a ton of random digits for you) - OR, can use a pre-made table of random digits ranging from 0-9 - it is equally likely for any particulra digit to come, but knowing what the next digit is is unpredictable. => each digit is unpredictable given the numbers before it, but in the long run, each digit appears about the same # of times Why are they grouped in 5s? - a convention that is followed to keep track of where the digits are [130] SIMULATION: DICE GAME OF 21 - Play with 6-sided dice - Each player continues to roll a die, totalling up the numbers he has rolled until they: a) decide to stop b) go over 21, and in this case, they lose, and the other player wins - Player with the highest score that is less than or equal to 21 is the winner (Ex) - Butler rolls the dice and continually does so until he chooses to stop - and he gets: - 4, 5, 4, 6, 3, 2 = 22 - lost - The other player automatically wins - randomizing device used was dice - Question: You are playing against an opponent who scored 18. What is the likelihood of you winning? - strategy that You (the 2nd player) should take on is continue rolling until you win or go beyond 21. => you will end up either winning, or go over the upper limit and thus lose Are we still using the dice now to predict this probability? - No; we will run a simulation for this 21 game for the following situation: if the opponent goes first and scores 18, what is the chances of the 2nd player winning? [131] USING RANDOM NUMBERS TABLE - what we are doing is choosing a set of numbers from the table at random and listing them out - Note: in the context of this game, you can only get values from 1 to 6. - So, all random digits that are 0, 7, 8 and 9 do not count - one trial is one set of digits, in this case => the number of times the player rolls has a maximum of 5, and a min. of 0. (ex) say you get 24513  all these 5 numbers are on the die, so from this set of random val's, we say that the player choose to roll 5 times (ex) say you get 99990 chose to roll 5 times and got 22, which is over 21 so we lose ex2. 67663 - 6 + 6 + 6 + 3 = 21 => chose to roll 5 times and got 21, which is over 18 so we won. ex. 62561 - 6 + 2 + 5 + 6 + 1 = 20 => chose to roll 5 times and got 20, which is over 18 so we won. => after 3 trials, can see we won in 2 out of 3 trials (not simulations), but have to do many more to really get a accurate depiction of the probability of winning (ex) - He used another statistical software package and run 1000 simulations: - found that 2nd player has about 72% chance of winning [132] HERE'S A BIGGER TABLE, ALL DONE BY SIMULATION - The table is showing: if the first player scores a given total, then what is the likelihood that the second player will win? - he deduced the percentages from running a 1000 trials
More Less

Related notes for STAB22H3

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit