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# File: MIT18_05S22_in-class5-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 5
Jerry
Slides 1,2 (1 minute)
Agenda: Variance of discrete RV start continuous RV
Slide 3 Studio 2 comments (4 minutes)
Decide on the fly whether to work the example or suggest they do on their own.
Jen
Slide 4 variance and standard deviation (4 minutes)
Highlight it's defined as the expected value of something
Discuss units
Slide 5 CLICKER question, order by variance (3 minutes)
Short discussion based on spread
Slide 6 CLICKER question, Var(X) = 0 ... (3 minutes)
Discussion: variance = sum of non-negative terms. If one is nonzero then so is variance.
Avoid the urge to keep talking about this
Slide 7 Variance example (paused slide) (6 minutes)
Work example -- directly, use board
Paused slide:
For E(X^2) - E(X)^2 formula.
--Work this quickly by adding to X^2 to the table
--Do not try to prove it.
--Remind class: It's in the reading, proof is easy
Slide 8 Clicker question & Table question (CQ: 1 minute, Table Q: 4 minutes:)
Paused slide
No discussion move right to table question
TABLE question: compute variance --staff should help them
Discussion -- scale matters,
Don't do the computation
Slide 9 Algebra of variance (2 minutes)
No proofs
Board questions will provide examples
Slide 10 BOARD questions: Var of bernoulli, binomial etc (Work 10 min. discussion 4 min.)
Discussion
They will have gotten these, so no need to go through solutions
Mention that using linearity requires independence
Slide 11 Continuous RVs intro (1 min)
Jerry
Slide 12 Calculus warmup (3 min)
Assume they have seen this --even if it's not fresh in their minds
Do not dwell on it.
Assure them we won't do hard integrals (though we may ask Wolfram Alpha to do them for us)
Thinking of integrals conceptually as sums is the key
Slide 13 Continuous random variables: range, pdf, cdf (3 min)
Emphasize f(x) is a density and f(x)dx is a probability
Slide 14 Visualization (2 min)
They will see pictures like these a lot --they should get good at understanding them.
Probabilities are computed by integration
Slide 15 Properties of CDF (3 min)
Same as discrete
Highlight F' = f
Slide 16 BOARD questions --pdf f(x) = cx^2 on [0,2] (Work 9 min. Discuss 5 min.)
Judge by how they do whether this requires much discussion.
Slide 17 Table discussion questions P(X=a) --NOT WITH CLICKERS (3 min)
(2 pauses)
Resist the urge to keep explaining
Slide 18 Table discussion questions valid cdf --NOT WITH CLICKERS (3 min)
Discussion
*** If we have time: ***
*** These slides will be repeated in class5b on the assumption that we won't get to them in class5.
Slide 19 Exponential distr. review (1 min.)
Just say this is the density. If is often used to model waiting times.
Slide 20 BOARD question Finish class
Discussion next time (maybe)