| Hand in Wednesday . = = = = = Probability , Ch. 10. 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 p. 256, 10.10 rolling die. Which obey the probability rules? p. 268, 10.44 Benford One more discrete probability Continuous sample spaces: p. 259, 10.15 Iowa Test Scores p. 269, 10.49 Did you vote? p. 269, 10.51 NAEP scores p. 269, 10.53 Friends On a separate sheet using http://www.whfreeman.com/bps4e "Probability " applet: If you do it jointly, one sheet for both people (I'll aggregate the results) p. 270, 10.55 runs of free throws p. 270, 10.56 a. For b, do 20 people 10 times, but do 320 people only twice. Record not only the proportion (.63 or whatever) but the fraction (like 201/320. 208/320 = .65 exactly) |
Read, to discuss
|
Optional |
Looking ahead (back)
Random variables with intervals
of outcomes
("continuous") Ch.10 (p. 256 on)
If the sample space is an interval of values (or the whole
line),
the way we assign probabilities to events is with a density curve
(Ch. 3, cf. Day 5 on) (remember density curves were
idealizations
of
histograms--of repeating the "experiment" many many times)
P(a < X < b) = the
probability that X is between a and b is the
area
under the density curve, between a and b.
We declare P (X = a) = 0 , so P(a < X < b)
= P(a < X < b)
Notation: Use capital letter for the random variable, the "label"
of the phenomenon. Use small letters for particular values it can
have. But this rule is often broken--Moore uses x-bar where many
(I)
would use X-bar.
HW: For A and B, Use Densities Handout, from
Day 5. Answers to old questions A
few paper copies of the HW
handout
are in class/ outside my door if you can't find yours.)
Change language from "description of a population of data" to "pick
an individual from the population, call the value X"
A. ("Uniform") X = number the spinner points to.
a) (example) The probability that the spinner points to a number
less than .6 = P( X < .6) = .6 .
b) P (.2 < X < .6) = ? Say
it
in words: ?
c) For what x is there probability .4 of being greater than x
?
(In notation: P(X > x) = .4. Find x)
B. Y = (number you get from) the sum of two spinners.
("Triangular") This is the same random variable as Y in
10.14, p. 259!
a) The probability that the sum is a number less than .6 =
P( ?
) =.18
P(Y > .6) = ?
b) P(Y <
1.6)
= ? P (Y <
1) = ?
P( 1 < Y < 1.6) = ?
c) P(Y > x) = .92 Find x: ?
(Hint: P(Y<x) = .08)
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Our most important probability model: NORMAL DISTRIBUTION
family.
Same techniques as before, only we ask "probability that one chosen at
random..." instead of "proportion of all..." Review Normal
techniques: Day 10 covers it all.
Take a random sample of size 1 from a population which
is
N(110, 25).
(Give an individual, chosen at random, the "Classic IQ
test", which
has a normal distribution, mean 110, s.d. 25. X is the
score
on the test.)
Find P(100 < X < 140), prob. that individual gets between
100 and 140. Work is on Day 10, what proportion.
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