#---------------------------------------------------------
# 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.