Summary: Math 4060 HW1 Key
Problem 2.2
Count the number of k point mutants of a string of length n.
Answer: clearly n
k
.
Problem 2.3
Suppose that two population members of length n over the binary alphabet disagree in m
positions. Then how many different children could be generated from them by uniform
crossover. Assume no mutation is used.
Answer: clearly 2m
.
Problem 2.4
Suppose that we are using size n tournament selection on a population of p strings that all
have different fitness. We rank the strings so that the most fit has rank one and the least
fit has rank p. Compute as a function of rank the probability that a string is one of the top
two in a tournament.
Answer: to do this problem we need to count the number of tournaments in which the
population member of rank c is first or second in his tournament divided by the number of
tournaments that can happen at all. For Mr. c to be first there must be n  1 people worse
