| Hand in Monday p. 233, 9.45 d antioxidants (review) p. 223 9.10 significance on Monday Postpone these two: p. 226, 9.13 hand strength, MP p. 231, 9.35 forest CO2 p. 226, 9.15 teaching techn. p. 232, 9.40 TV ads, block design. Use the Applet, to assign your subjects. Number your Women and your Men, and show their numbers as well as the group they're in. p. 229, 232, 9.27 and 9.39 wine, beer, spirits two ways - - - - - - - - - - Hand in Monday: "Ethics": Read Data Ethics, pp 235-242. Find at least one other person in the class, and together discuss one of these questions. Write up your answers (If you have consensus, fine! If you disagree, say who thinks what). pp. 242-245, # 4 or 5 or 9 or 11 or 13 or 14 or 17 = = = = =Postpone Chapter 10 = = = = = = = = 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. 261, 10.16 Grades RV p. 266, 10.37 Land in Canada 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. 252, 10.6 and 10.7 D&D, 4-sided dice p. 267, 10.42 Race and ethnicity |
Read, to discuss p. 232, 9.38 spine fractures You lack the
information to make a complete design (i.e. how many women at each
hospital.) Sketch in what you can. |
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"
"Probability" of particular something
happening:
proportion
of times it would happen in a very long series of (independent)
repetitions
of the phenomenon.
Applet: Probability
(independence:
outcome of one trial (repetition) must not influence the outcome of any
other.)
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)
Pick one person from U.S. Pop. (Age 25 +)
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Discrete models: (Can make a list
of all members of the sample space) Make the
list, and
Assign a probability to each outcome (>0)
so they add to 1. (Sometimes equal values make
sense.)
Prob. of an event is sum of
prob's of its outcomes.
Phenomenon: Flip coin twice.
S1 = {HH, HT, TH,
TT} S2
= {0, 1, 2} number of heads
S3 = {Y, N} both are heads?
Sample space | HH | HT | TH |
TT
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Prob's
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.25| .25| .25| .25| P(tail followed by head)=?
Sample space | 2
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1 | 0 | P(at
least 1 tail)=? P(1 of each) = ?
Prob's
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.25| .50 | .25| P(at least 1 Head)=
?
P(2 Heads) = ?
Sample space | Y
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N |
Prob's
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.25| .75 |
Often the sample space is naturally expressed in numbers, thus
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."
Flip coin twice. R.V. X
= number of heads:
Distribution given by table.
x| 2 | 1 | 0 |
P(X=x)
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.25| .50 | .25|
P(X >
1) = ?
Words: Prob that #
heads is >
1
P(X = 2)
=
?
Prob that # heads is
2
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