Math 151, Spring 2011
Jo Hardin, HW #4
Homework due on
Thursday, February, 10th, start of class.
1. DeGroot (3
rd
or 4
th
ed.), section 2.1: # 6, 8, 16
•
2.1 # 16: Consider again the shopper described in Exercise 4. On each purchase,
the probability that he will choose the same brand of toothpaste that he chose on
his preceding purchase is 1/3, and the probability that he will switch brands is
2/3. Suppose that on his ﬁrst purchase the probability that he will choose brand
A is 1/4 and the probability that he will choose brand B is 3/4. What is the
probability that his second purchase will be brand B?
2. DeGroot (3
rd
or 4
th
ed.), section 2.2: # 13, 14, 15, 16
3. DeGroot ( 4
th
ed.), section 2.3: # 6, 12, 15 (3
rd
ed., section 2.3: # 10, 16, 19)
4. Additional problem in R: Even more HardyWeinberg equilibrium
# Three genotypes:
P
(
AA
) =
p
=
PAA,P
(
Aa
) = 2
*
q
=
PAa,P
(
aa
) =
r
=
Paa
;
# Note that
r
= 1

p

2
*
q
calcnextgen = function(PAA, PAa, Paa, u=1, v=1, w=1) {
PAA2 = u*(PAA*PAA*1 + PAA*PAa*.5 + PAa*PAA*.5 + PAa*PAa*.25)