When talking about mathematical modeling, we used the simple example of an allele A mutating to allele a at rate . The frequency of A in the next generation is then given by the recursion equation:

frequency of A next generation = A's frequency now proportion of A that mutates to a

pt+1 = pt - pt

a) If the rate of back mutation of a to A is , write the recursion equation for pt+1 that includes both forward and back mutation (i.e. and ). In your equation, express pt+1 as a function of pt only (i.e. not qt)

b) Solve for the equilibrium allele frequency of A (???????? ) by setting pt+1 = pt = ???????? and solving.

c) If = 10-6 and = 10-5, what is the equilibrium frequency of A? Does this value make sense (i.e. explain why it is closer to zero than to 1)

Question: 2

Blackmoor Golf Club Members

The golf shop is holding a raffle to win a TaylorMade R9 10.5 Regular Flex Driver ($300 value).

Tickets are $5.00 each. Only 80 tickets will be sold.

Please see the golf shop to get your tickets!

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John Underpar buys a ticket.

a. what are Mr. Underpar's possible monetary outcomes?

b. what are the probabilities of the possible outcomes?

c. Summarize Mr. Underpar's "experiment" as a probability distribution.

d. what is the mean or expected value of the probability distribution? Explain result.

e. if all 80 tickets are sold, what is the expected return of the club?