Hw11: Probability

Before you tackle the homework, remind yourself of our general hw policies.

Reading: Rosen chpt 5.

1. (1pt  ) p. 361 #10 (2D*3S) (as a fraction in lowest terms -- no need for a calculator !-)
2. (1pt  ) p. 361 #12 (one ace)
3. (2pts) p. 376 #8 (list permutations).
4. (2pts) p. 376 #18 (birthday-of-week)
5. (4pts) p. 378 #40 (constant-time check for ordering (monte carlo))
6. (4pts) p. 392 #6 (expected lottery ticket price). As its "value", compute its worth minus its cost.
7. (4pts) p. 392 #12 (expected rolls 'til 6)
8. (2pts) p. 392 #16 (show non-independence)
9. (3pts) Suppose Subway has three categories of sandwiches: budget, standard, premium which sell for $3.20,$4.30,$5.40 respectively. It turns out that customers each type of sandwich 30%, 50%, 20% of the time respectively. Further, every sandwich yields two stamps, and sixteen stamps can be redeemed to buy a sandwich for only $1.18. (We'll ignore the free soda.)

   1. What is the expected worth of a stamp? Ignore and see (c) instead: What is the expected cost of a stamp?

   2. Suppose that only 75% of people use the distribution above. The remaining 25% tweak the stamp system to their advantage: they always buy budget sandwiches, but exchange the stamps for premium sandwiches.

      Under this new distribution, what is the expected worth of a stamp? Ignore and see (c) instead: What is the expected cost of a stamp?

   3. 1pt extra credit: Subway would like to know the effective discount they're giving through their stamp program. For each of the two distributions, what is the expected cost of a sandwich? Assume that each individual pays with stamps 1/8 (oops, 1/9 -- unless the clerk mistakenly gives you stamps on a sandwich which you just redeemed via stamps) of the time.