Construct a tree diagram for the test.

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Answer 1

Question

Chapter 5, Problem 91CP

a.

To determine

Construct a tree diagram for the test.

b.

To determine

List the intersection probabilities in a contingency table.

c.

To determine

Compute the probability that the person is truly HIV positive given that the person gets positive result.

d.

To determine

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

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T1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an independent set and m(G) = |E(G)|. (i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The neighborhood of a vertex in a triangle free graph must be independent; all edges have at least one end in a vertex cover. (ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you may need to use either elementary calculus or the arithmetic-geometric mean inequality.

We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…

Negate the following compound statement using De Morgans's laws.

Answer 2

Question

Chapter 5, Problem 91CP

a.

To determine

Construct a tree diagram for the test.

b.

To determine

List the intersection probabilities in a contingency table.

c.

To determine

Compute the probability that the person is truly HIV positive given that the person gets positive result.

d.

To determine

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 5, Problem 91CP

a.

To determine

Construct a tree diagram for the test.

b.

To determine

List the intersection probabilities in a contingency table.

c.

To determine

Compute the probability that the person is truly HIV positive given that the person gets positive result.

d.

To determine

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 5, Problem 91CP

a.

To determine

Construct a tree diagram for the test.

b.

To determine

List the intersection probabilities in a contingency table.

c.

To determine

Compute the probability that the person is truly HIV positive given that the person gets positive result.

d.

To determine

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 5, Problem 91CP

a.

To determine

Construct a tree diagram for the test.

b.

To determine

List the intersection probabilities in a contingency table.

c.

To determine

Compute the probability that the person is truly HIV positive given that the person gets positive result.

d.

To determine

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

Answer 6

Chapter 5, Problem 91CP

a.

To determine

Construct a tree diagram for the test.

Answer 7

Chapter 5, Problem 91CP

a.

To determine

Construct a tree diagram for the test.

Answer 8

b.

To determine

List the intersection probabilities in a contingency table.

Answer 9

b.

To determine

List the intersection probabilities in a contingency table.

Answer 10

c.

To determine

Compute the probability that the person is truly HIV positive given that the person gets positive result.

Answer 11

c.

To determine

Compute the probability that the person is truly HIV positive given that the person gets positive result.

Answer 12

d.

To determine

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

Answer 13

d.

To determine

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

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Construct a tree diagram for the test.

Solution Summary: The author explains that the tree diagram is a graphical representation of sample points. The first branch shows whether or not the selected person is HIV positive.

Concept explainers

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Construct a tree diagram for the test.

List the intersection probabilities in a contingency table.

Compute the probability that the person is truly HIV positive given that the person gets positive result.

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

Want to see the full answer?

Chapter 5 Solutions

Construct a tree diagram for the test.

Solution Summary: The author explains that the tree diagram is a graphical representation of sample points. The first branch shows whether or not the selected person is HIV positive.

Concept explainers

Videos

Construct a tree diagram for the test.

List the intersection probabilities in a contingency table.

Compute the probability that the person is truly HIV positive given that the person gets positive result.

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence. Explain the reasons for positive results are more likely to be in error if the prevalence is lower.

Want to see the full answer?

Chapter 5 Solutions

Construct a contingency table with frequencies for 10,000 people with 10% and 1% prevalence.

Explain the reasons for positive results are more likely to be in error if the prevalence is lower.