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# File: MIT18_05S22_in-class4-script.txt
# Author: Jeremy Orloff
#
# MIT OpenCourseWare: https://ocw.mit.edu
# 18.05 Introduction to Probability and Statistics
# Spring 2022
# For information about citing these materials or our Terms of Use, visit:
# https://ocw.mit.edu/terms.
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Class 4
Jerry
Slide 1
Slide 2 Agenda/Announcements. (12 minutes)
Finish squirrel problem
Have slides from last time ready
Give them 6 minutes to work --announce this with problem
Slide 3 Review (2 minutes)
Just state. They will get practice in concept questions and later
Note: We the cdf will be much more prominent when we do continuous distributions
Slide 4 Example random variable as payoff function (5 minutes)
--Story: roll 4-sided die: pay -2, -1, 0, 4 for 1,2,3,4
Discuss notation X=a, X<=a
THERE IS A PAUSE IN THIS SLIDE.
Do question about F(a) and p(a) as call and response
Show answers after pause
Slide 5 Properties of PMF and CDF (2 minutes)
0 <= pdf <=1, sums to 1
cdf: increasing from 0 to 1
Slide 6 Plot of pmf and cdf (1 minute)
Just note the properties
Slide 7 CONCEPT questions, cdf, pdf (1 minute each.)
PAUSED slide
There are 2 of them separated by a PAUSE
DON'T DWELL ON THESE
For problem 2: can write on board: P(X=3) = F(3) - F(1) --but don't dwell
Slide 8 Meaning of expected value (6 minutes)
Slide is crammed with text. This is for reading outside of class.
Let the class know this is for reading later.
Do not go through the preliminary 5 experiment example.
Go through the expected part carefully
Slide 9 Expected value definition (3 minutes)
Definition and properties
Just note that the properties follow easily from the definition and are in the reading.
Slide 10 Expected value examples (6 minutes)
PAUSED SLIDE (6 slides)
Do these as table questions
ex 1. Just have them say what they would compute
e.g. 3*1/4 + 4*1/2 + 5*1/8 + 6*1/8
ex 2. They should compute to answer
** Important result DON'T DWELL. This is also a later board question
ex 3. Ask for numerical answer
If after 3:15 skip this in favor of helping them through the similar board question.
Slide 11 E[h(X)] example (2 minutes)
Several pauses in this slide (3 slides)
Do E(X) as table question
Show answer
Do E(X^2+X) as a table question
Show answer -- point out line 5 comment
Jerry: introduce, Jen: discussion
Slide 12, 13 BOARD questions (15 minutes: 10 work, 5 discussion
DO BOTH BEFORE DISCUSSING
Stay standing for next problem.
10 minutes for work, 5 minutes discussion.
Take display off full screen so can show both
** No need to discuss 1 if they all get it.
** For 2, no need to compute the expected payouts. Just discuss the framing bias
Jen
Slide 14 BOARD question (10 minutes: 5 work, 5 discussion)
Discussion:
Do by linearity of expectation.
Notes: A permutation where no one ends up in the correct position is called a derangment
Slides 15-17 Deluge of distributions (3 minutes)
Emphasize importance of understanding Bernoulli
Describing Binom as a sum of Bernoulli -- this is where the time will be spent.
No repetition! Assure them that we will have lots of practice with these distributions
Don't dwell on geometric --we'll see plenty of it in the future
Realistically we might not get here
Slide 18 Board questions (10 minutes)
Do the problems. Solutions on Tuesday
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There won't be time
Slides 19-20 Fallacies
Monte Carlo 1913 --came up black 26 times in a row
By #15 people were betting big on red. Doubling and tripling bets
in belief that red was more and more likely
House made a lot of money
HOT HAND --maybe
Slide 21 Amnesia
ONLY IF TIME (HAHA)
Prove this for them.