| Hand in Wednesday .
Bring remaining sample exam questions, other questions. p. 226, 9.13 hand strength, MP p. 231, 9.35 forest CO2 = = = = = Probability , Ch. 10. Rearranged a bit. Though we spent little time in class on these, they should not be hard, if you read to p. 256. p. 249, 10.1 Texas Hold'em p. 249, 10.3 50, 200 Random digits. Bring your result for (b) to class to compare with others. I did it twice, got .06, .09 Applet: Probability p. 250, 10.4 Probability says.. p. 265, 10.30 Sample spaces, free throws p. 252, 10.5 Sample spaces p. 254, 10.9 Canadian languages p. 254, 10.12 Watching TV p. 266, 10.37 Land in Canada Postpone the rest p. 265, 10.31 Probability models? Note, you only are checking whether the model is legitimate, not whether it's correct for the phenomenon described! p. 261, 10.16 Grades RV p. 252, 10.6 and 10.7 D&D, 4-sided dice p. 267, 10.42 Race and ethnicity |
Read, to discuss
|
Optional p. 226, 9.14 matched and not, more practice |
Principles of designing an experiment: Compare
groups with different treatments: Control as much as you can, to make all
the groups the same except for treatments, Randomize
the rest; Use enough subjects
to average out bad "chance" .
"Randomized comparative experiment". Issues,
vocabulary....see previous days
Discuss acupuncture, 3
treatments (music, acupuncture wrong, acupuncture right)
Really 2 sub-experiments; Acupuncture right vs.
acupuncture wrong is blinded placebo-controlled measurement
of effect of correct acupuncture. Acupuncture wrong vs. music
is measurement of the placebo effect of having needles stuck
in you.
A little problem: I just read that listening to music has
been shown to lessen pain. So what can we do about Music/none as
a confounding variable here?
Probability
Models
: (p. 250-256)
Random phenomenon,
described by
Sample space S: set
of all possible outcomes (no overlap of descriptions)
Event: any
outcome
or set of outcomes
Probability model:
S, and a way of assigning a probability to each event.
Sample space depends on what you want to know:
Phenomenon: Flip coin twice.
S1 = {HH, HT, TH,
TT} S2 = {0, 1, 2} number of
heads
S3 = {Y, N} both are heads? \
We looked at the probabilities for
these, implicitly using the "common sense" rules for proportions just
below.
Probability rules: pp. 253, in
words, then in notation.
A an event in sample space S, P(A)
is "the probability
that A occurs"
These rules are all true for
proportions
in long run (Probabilities), proportion of counts,
proportions of areas.
1. 0 <
P(A) < 1
(any probability is a number between 0 and 1. )
2. P(S) = 1
(all the outcomes together have total probability 1)
3. A and B
are
disjoint if they have no outcomes in common (can't happen
simultaneously.)
If
A and B are disjoint, their probabilities add: P(A or B) =
P(A)
+ P(B)
4. For any
event A,
P(A
does not occur) = 1 - P(A)
Discrete models:
Assign a probability to each outcome (>0)
so they add to 1. Prob. of an event
is sum of
prob's of its outcomes.
Random Variable:
(X, Y, Z...) Variable whose value is a numerical outcome of a
random
phenomenon.
Probability distribution of X tells
us what values X can take and how to assign probabilities to them.
If X has a finite number of
possible values (Discrete distributions), nothing new except
notation.
P(X < 2) is "Prob.
that X is less than 2."
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