Comments on Assignment 4

Problem 1: (b) Approximate g by simple functions.

Problem 2: (a) Write f a as limit of simple functions.
(c) Dropped. The function g(x) = (# 7's - # 6's)/(# 8's) will work.

Think of the decimal expansion of a "random" number x in [0,1]
as determined by repatedly rolling a 10-sided die. (This is not 
quite right because some numbers have more than one decimal 
expansion, i.e., sequences ending in "999..." do not appear
as decimal expansions. But those numbers form a set of measure zero.) 
We will later see that the integral (mean) of f is 1/10, and 
that f(x)=1/10 for almost every x. This is an example of the 
Law of Large Numbers.

Problem 5: (a) It may help to write out the cases n=2,3,4.

(b) Dropped.  The forgetful secretary stuffs a bunch of
(personally addressed) letters at random into (named) 
envelopes.  p_n is the probability that not a single invitation 
ends up in the right envelope.