5.2 (Central Limit Th. and friends) generalizes the idea of averaging
(or summing) n independent identical random variables from the simplest
case where each is a Bernoulli trial (outcome either 0 or 1), to any
X with any distribution. Nothing should be a big surprise.
Note: They use capital letters for random
variables and small letters for specific values, except they use
small xbar in this section where they should be using Xbar. (Typesetting
problem??)
Xbar = (X1
+ X2 +...+ Xn )/n
, independent, identically distributed.
The X's are (usually for us) a SRS from a population with distribution
of X (assuming pop. is 10 times n)
The distribution of all possible
Xbars is called the Sampling distribution of Xbar.
| µXbar = µX sigma Xbar = sigmaX ÷ sqrt(n) |
| If X is normal, then Xbar is normal |
| If n is large, then Xbar is approximately normal (Central Limit Theorem) |
HW 27 Read 5.2 For this homework, the
contents of the boxes, pp. 399, 400, 402. (summarized in yellow table above)
We will consider the consequences of a general linear combination of
independent normal random variables (p.401) next time.
Down the line: We will skim through Weibull dist. (pp.406-7)
and 5.3, and continue with 6.1.
| Hand in:
Binomial review If you didn't get 5.9, do it now. Watch effect of changing n. Sec. 5.2 5.28 axle diameter (mean, s.d.) 5.27 coal mine filters Note that the laboratory does NOT know the actual weight, and its scales are not perfectly accurate. Nonetheless... 5.29 coke--1 vs. six. 5.30 hypokalemia. Anybody ever been sent back for a retest? 5.35 NOX--backward. Recall, like ex.1.27 p.78 Question on reading: Why is the normal model "good" for so many observed data sets? (Hint: answer is on pp. 402-3) Will be assigned next time: Linear combinations of independent normal r.v.'s (as p. 401) 5.38 resistances add 5.39 compare chicks 5.41 muX - muY 5.44 delay avoidance+work methods 5.45 X+Y couples. |
Read, discuss
5.19 blacks represented?
next time: 5.40 Methods A and B |
Optional
Sec.5.2 (more practice) 5.26, ACT,1&50 5.37 kindergarten--backward calc.
next time: 5.42 X+Y+ Z |
| Sievers home | Math251-Fall01/DayP27.htm | 11/1/01 |