Math 300 , Spring 2002, Day 23, W, March 27 Hit reload to get most current versionAfter class

Variance of Hypergeometric, with handout
What are the Cov terms?  Look at mult. table: 2 times each of the items below the  x² diagonal.
    a   b   c   d
a |
b |
c |
d |

Application of discrete dist:  Bird calls.  (Due Friday) We estimate a parameter from the data, construct the resulting member of a distribution family, then compare it to the actual data to see if the mechanism of that distribution gives a reasonable fit.

Quiz Monday: Closed book, Expected value stuff, chosen from:
Deriving E of Poisson, Var of Poisson  from E(X(X-1)) and E(X),
Proofs for Var and Cov alternate formulas.  Var(X+Y) = (derivation)
Independence and E(XY), Cov(X,Y)

HW:  Read 4.1.
Bird calls handout.  (Due Friday)
The rest due Monday
p. 103-4, #1 thru 6
Read ahead pp.104 to 114.  (You can do the following problem whether or not the reading makes sense.)
p. 114 graph fig. 16 is wrong in my text. Graph it, and see if yours is right or wrong.  (The formula is just above the graph)

Will continue from here, Friday
Ch. 4, Continuous distributions--outcome is a measure, not a count.
Questions?  f(x) on p. 95 and g(x) on p. 96 --piecewise-defined functions
   Density curve:  f(x) > 0, with total area under f(x) = 1  "Probability density function" = "pdf"
Probability = Area under the curve.  P(a<X<b) = area between a and b.
We'll use integration to find areas under the curve (usually.  Normal density can't be integrated with a formula).

The area under the curve being 1 means that as x goes toward plus, or minus, infinity, f(x) goes to (or is) 0.

 4.1:  Newish from calculus: Piecewise defined functions.  You have to make sure you're integrating the right formula; break the integral at points where the formula changes.

Any function g(x) > 0 can be made into a density by dividing by a number that makes the result have total area 1.
   What number to divide by?  The area under g(x).

I won't try to put the calculus computations on the webpages--too time-consuming for me.  So take good notes, check with one another for "repairs" to notes.