| 9|0.0, 0.0, 4.5, 6.4
8|6.4, 8.2 7|3.6, 7.3 6|7.3 5|1.8, 9.1 |
Making up points: You can earn back up to 50% of lost points
on a problem by writing a new exam problem that tests the same things I
was testing for, and doing the problem correctly. Hand in the new
problem(s), the solution(s), and your (old) exam.
For problem 9, the proofs, learn them, and do them orally on the board, with me asking at each stage why you did what you did, why it is "legal." Please ask me for help beforehand on any of these. Due Mon. Oct 29--longer than you should take, but plenty of slack.... |
Sec. 4.3--Random Variables: If the sample space is a list (or continuous interval) of numbers, we use the notation of a variable (X, Y, W, Z) to express probability statements. (as P(X < 3)). This is more complicated than a calculus variable because the variable carries the "baggage" of probabilities attached to values it can take on. (Some people dislike the name "variable" but we are stuck with it because of history. It parallels the use in data for some aspect of a population that we measure.)
We can use graphs with the sample space on the horizontal axis, and
a curve or histogram above, to model the probability distribution.
The area above an interval then represents the probability of the interval.
(The whole area = 1)
| Probability distribution: | Defined using: | Graphic representation: (Area under is 1) |
| Discrete distributions | table (sometimes formula (later)) | "probability histogram" |
| Continuous distributions | (formula) | "density curve" |
Read 4.3, all. Read ahead 4.4. Next, Continuous R.V.'s (including Normal), and start 4.4.
| Hand in:
A. Current events event. Read the Census clipping along with "capture-recapture sampling," pp.275-6. Write a sentence or two saying whether you agree with the Republicans or the Democrats. - - - - - - - - - - - Random variables--Discrete 4.40 household inhabitants 4.42 sum of 2 dice Hints: Think of a red die and a black die. A two-dimensional graph is a good way to arrange this: on the horizontal-axis mark the possibilites for the red die (1,2,3,4,5,6) , and on the vertical axis mark the possibilities for the black.(1,2,3,4,5,6). Then each integer pair, intersection on the grid, stands for a possible pair; (1, 3) means 1 on the red and 3 on the black. Note the geometry of which pairs have equal sums. 4.43 3 student reps-->#opposed. For part a, I suggest making a tree of the possibilities/probabilities. The first branching will be for student A: support or opposed? Once that is decided, we branch for student B: support or opposed?; likewise for student C. What assumption do you make to find the probabilities? |
Read, discuss
4.31 age/education table |
Optional
Random variables--Discrete p. 322 4.39, 4.41 (MOTS, more of the same) |
| Sievers home | Math251-Fall01/DayP21.htm | 10/19/01 |