MATH 251, Probability and Statistics I, Fall 2001, Wed. Oct. 24, Day 23 final version

Making up exam 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 6, 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.

Diaconis Article?
Keep your problems A and B (or the whole HW paper)

If  X and Y are random variables,  and we do  linear things to them, we can (often) find the mean and variance of the result, just
from knowing the original mean and variance (without having to find the whole distribution of the result.)  I'll call these rules
the Algebra of Means and Variances.
Means: p. 334    Variances: p. 337
Rules 1 are for a linear transformation a+bX of one R.V. (cf. p. 57 for data),
Rules 2 for a linear combination X + Y

 Read Sec. 4.4.  We will skip 4.5 for now and go next to ch. 5.  Please read ahead 5.1.
Hand in:
  Algebra of means, variances (rules, p334, p. 337)
Do C, D on the Algebra of means and variances page. 

4.59, 4.65 auto chassis
4.69 F & C
4.67 b, c sales and profits  Use the answers to a from the back of the book. 
4.70  Y-X, (X+Y)/2
4.72  insurance (use from previous problems,  mean $303.3525, s.d. = 9707.57, variance = 94,236,826.64) (The behavior of the mean of n indep. identical r.v.'s is important--we'll be looking at it explicitly in ch. 5) . 


Proofs:  Write up in detail the proofs for the mean and variance of Y=a+bX,  repeating or extending the class work.  (Use big sigma, and parallel to it the sum written out for n=3.)
 		 Read, discuss 
 

 

 Optional 

 
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