 
Summary: NOTES ON "ROTTEN EGGS"
PROF. GREG W. ANDERSON
This is a summary of the "rotten egg" examples from class on October 6, 2011
along with some additional material which I hope begins to explain the notation I
use for joint, marginal and conditional probability functions.
Setup for the example
Suppose that in one dozen eggs there are exactly four rotten eggs. Let X be the
number of rotten eggs in a sample of 2 without replacement. We throw the eggs
away after noting how many are rotten. Then, let Y be the number of rotten eggs
in a further sample of 1 without replacement.
The joint distribution of X and Y
The joint p.f. of X and Y . We have
fX,Y (x, y) = Pr(X = x and Y = y)
=
4
x, y, 4  x  y
8
2  x, 1  y, 5 + x + y
12
2, 1, 9
