| Hand in Wednesday .
Bring remaining sample exam questions, other questions. = = = = = Probability , Ch. 10. p. 249, 10.3 50, 200 Random digits. Bring your result for (b) to class to compare with others. I did it 4 times (four sets of 200 tosses) , got .06, .09, .07, .14! Applet: Probability Postpone all the rest: p. 250, 10.4 Probability says.. p. 254, 10.9 Canadian languages p. 254, 10.12 Watching TV 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. 261, 10.16 Grades RV p. 252, 10.6 and 10.7 D&D, 4-sided dice p. 267, 10.42 Race and ethnicity (added to last time's list) p. 256, 10.10 rolling die. Which obey the probability rules? p. 268, 10.44 Benford One more discrete probability |
Read, to discuss
|
Optional |
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 DID NO NEW MATERIAL MON: Exam 3 stops here.
Start here next:
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."
New/recap:
Probabilities
follow the "common sense" rule for proportions of a whole. Same
rules for proportions of areas, proportions of counts, proportions in
histograms, proportions of times in the long run something would
happen.
Two principles for assigning
probabilities:
--Sometimes, a properly chosen sample space will have equally likely
outcomes. You can use this to find other probabilities.
--If you pick an individual at random from a population, the
probability that one individual will be XYZ is the same as the
proportion of XYZ's in the population.
Next: Continuous Sample Spaces.
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