| Hand in Monday . = = = = = Probability , Ch. 10. (If you didn't for today or you did it wrong: 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) .Nothing more to hand in. BUT.Please read all of Ch. 10 and review Normal Distribution! p. 261, 10.16 Grades RV p. 252, 10.6 and 10.7 D&D, 4-sided dice Continuous sample spaces: ***For A and B, Use Densities Handout, from Day 5. Answers to old questions 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) *** p. 259, 10.13 uniform, 0-1 (Note, this is distribution A on the handout) p. 259, 10.14 sum of two uniform (Note, this is distribution B, "Triangular", on the handout) pp. 236-7 10.48 and 10.50 uniform on 0-2 (This corresponds to a single spinner with its edge labeled with values going from 0 to 2, rather than the 0 to 1 we used in our homework up to now. Use the area-of-rectangles formula to find the probabilities.) |
Read, to discuss
|
Optional |
Chapter 10, Probability (intro) , continued
Details Day 24
No new material today. Continue with this Monday
New today: Random Variable Day 24
and Recap Day 25
Example of an equally likely sample space, which can be used to find
probabilities for another: p.251, Ex. 10.4, 5, Two dice.
So far, everything was for Discrete sample spaces (you can list the outcomes)
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
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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