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# File:   MIT18_05S22_in-class5b-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 5b

Jerry
  Slide 1,2. Agenda (1 min.)

  Slide 3. Exponential random variables (2 min.)
    Define and note that knowing f(x) gives all the information about the random variable.

  Slide 4 Board question (work 9 min. discuss 4 minutes) 

  Slide 5 Uniform (2 min)
    Define. 
    Uniform because constant in its range

  Slide 6 Normal (5 min)
    Formula is shown. 
    Note, symmetry about mean.
    Show applet: vary mu = location, sigma = shape

Jen
  Slide 7. Table question (work 8 min., discuss 4 min)
    Play with applet.
    Encourage them to do part (d) both with the pdf and cdf
    Discussion: just get the class answers to a,b,c --will discuss on next slide
       For (d) show applet using cdf.

  Slide 8. Normal probabilities  (4 min.)
    Note: Consistently will use Z for standard normal RV
     
  Slide 9. Manipulating random var (5 min)
    Paused slide
    Acknowledge this is tricky
    Emphasize need to use cdf
    Go through solution carefully before showing solution on second half of the slide

  Slide 10. Board question (work 10 min., discussion 10 min.)
    Discussion: Only go through the ones that gave people trouble

  Slide 11. Histograms (2 min)
    Brief: Note studio will be about histograms
    Just that there are two types and R can make them
    Vertical scales are different
    Look the same for equal width bins, not otherwise.
           
  Slide 12. Board question: Finish class doing this