Question

In: Advanced Math

A group of k Vikings independently set out to make a new home. Each Viking has...

A group of k Vikings independently set out to make a new home. Each Viking has a copy of the same map, showing n islands. Each Viking decides to set sail for some random island. If two or more Vikings land on the same island, they have a battle. (No matter how many Vikings land on that island, it counts as one battle.)

(a) How many battles do we expect will occur? (Hint: Fix a single island, what is the probability of no viking ever landing there? What about exactly one viking reaching this island? What is the relationship of these events and there being a fight in the island?)

(b) You should have obtained a closed formula that depends on n and k. For both formulas, consider the cases in which there is only one island on the map. Do your solutions confirm the intuitive answer for this case? What if there’s only one Viking? What answers do you get for 400 Vikings and 100 islands?

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Assume you have just taken out a new home mortgage. You will borrow $200,000 and make...
Assume you have just taken out a new home mortgage. You will borrow $200,000 and make equal annual payments for 20 years. a. If the interest rate is 10% per year, how much will the payments be if you pay interest on the unpaid balance each year? b. Construct an amortization schedule for the first two years. (There should be 5 columns: end of year, Payment, interest, principal repayment, balance; remember, you borrow today, the end or year 0) c....
Consider two lobster fishermen from Maine. Each has to decide, independently, how many traps to set....
Consider two lobster fishermen from Maine. Each has to decide, independently, how many traps to set. Each can set either 5 or 15 traps. The more traps one fisherman sets, the higher the cost of fishing for the other. Their earnings for each combination are in the table below. The first number in parentheses is the payoff for Fisherman A. Fisherman B 15 Traps 5 Traps Fisherman A 15 Traps ($6, $6) ($14, $3) 5 Traps ($3, $14) ($12, $12)...
Treat each of the following statements independently, and state whether they make economic sense or not....
Treat each of the following statements independently, and state whether they make economic sense or not. a. “Recent reductions in airfares among the major airlines has increased the demand for air travel." b. “The Covid-19 pandemic has decreased the demand for air travel."
Suppose that Serena has a .7 probability of defeating Venus in a set of tennis, independently...
Suppose that Serena has a .7 probability of defeating Venus in a set of tennis, independently from set to set. For questions 1 – 3, suppose that they play a best-of-three-set match, meaning that the first player to win two sets wins the match. 1. Determine the probability that Serena wins the match by winning the first two sets. 2. Determine the probability that the match requires three sets to be played (meaning that each player wins one of the...
Case study A new staff member has commenced at the group home. On Thursday, she does...
Case study A new staff member has commenced at the group home. On Thursday, she does the following things: • Reminds Jun-Wei to have a shower and how to wash properly. • Helps him dry his back only. • Accompanies him on a walk to visit a friend. • Asks him to fry a steak in the frypan while she supervises. • Sends him into the shop to buy six apples and four bananas with a $50 note, while she...
2. A rancher has set out to fence off a new rectangular pasture for her horses....
2. A rancher has set out to fence off a new rectangular pasture for her horses. She has 1000 feet of fencing to fence off as large an area as possible. She wants to give the horses some water access, so she is building the pasture along a river, which will not need fencing. (a) Write a function, P(x), that describes the area of the pasture as a function of its length, x. (Don’t need Python for this.) (b) Plot...
Out of the 10 k from Home depot and Lowes from year 2018 1. What is...
Out of the 10 k from Home depot and Lowes from year 2018 1. What is the percentage increase/decrease in revenues? 2. What is the return on assets ratio? 3. What is the return on common stockholders’ equity ratio? 4. What is the percentage increase/decrease in total assets? 5. What is the current ratio? 6. What is the current cash debt coverage ratio? 7. What is the amount of free cash flow? 8. What is the payout ratio? 9. What...
Mr Hartup is living independently in his own home. He has been diagnosed with Alzheimer’s and...
Mr Hartup is living independently in his own home. He has been diagnosed with Alzheimer’s and is becoming increasingly vague and forgetful. His primary carer is his daughter, Janice, who has moved into Mr Hartup’s home to assist him. You have been supporting Mr Hartup for the past six months, visiting on a daily basis and according to his care plan, under personal care you have been providing medication and assisting with his personal hygiene. Question: Help Mr. Hartup find...
Mr Hartup is living independently in his own home. He has been diagnosed with Alzheimer’s and...
Mr Hartup is living independently in his own home. He has been diagnosed with Alzheimer’s and is becoming increasingly vague and forgetful. His primary carer is his daughter, Janice, who has moved into Mr Hartup’s home to assist him. You have been supporting Mr Hartup for the past six months, visiting on a daily basis and according to his care plan, under personal care you have been providing medication and assisting with his personal hygiene. Question: Use a motivational approach...
Let G be a group. Consider the set G with a new operation ∗ given by...
Let G be a group. Consider the set G with a new operation ∗ given by a ∗ b = ba. Show that (G, ∗) is a group isomorphic to the original group G. Give an explicit isomorphism.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT