Fundamentals of Biostatistics
8th Edition
ISBN: 9781305268920
Author: Bernard Rosner
Publisher: Cengage Learning
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Textbook Question
Chapter 3.7, Problem C.2RE
What are the PV+ and PV− of a screening test? How does PV differ from sensitivity and specificity?
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Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
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Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
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In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Chapter 3 Solutions
Fundamentals of Biostatistics
Ch. 3.6 - What is the frequency definition of probability?Ch. 3.6 - What is the difference between independent and...Ch. 3.6 - What are mutually exclusive events?Ch. 3.6 - What is the addition law of probability?Ch. 3.6 - What is conditional probability? How does it...Ch. 3.6 - What is relative risk? How do you interpret it?Ch. 3.6 - Prob. B.1RECh. 3.6 - Suppose the rate of type II diabetes mellitus (DM)...Ch. 3.7 - What is the sensitivity and specificity of a...Ch. 3.7 - What are the PV+ and PV of a screening test? How...
Ch. 3.7 - Prob. C.3RECh. 3.7 - What is Bayes rule? How is it used?Ch. 3.7 - Prob. D.2RECh. 3.7 - Prob. D.3RECh. 3.7 - Prob. D.4RECh. 3.10 - Suppose that of 25 students in a class, 5 are...Ch. 3.10 - Suppose 50 HIV-positive men are identified, 5 of...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Consider a family with a mother, father, and two...Ch. 3 - Prob. 11PCh. 3 - Suppose an influenza epidemic strikes a city. In...Ch. 3 - Suppose there is a 20% chance each child will get...Ch. 3 - Suppose there is a 20% chance each child will get...Ch. 3 - Suppose there is a 20% chance each child will get...Ch. 3 - Mental Health Estimates of the prevalence of...Ch. 3 - Mental Health Estimates of the prevalence of...Ch. 3 - Mental Health Estimates of the prevalence of...Ch. 3 - Mental Health Estimates of the prevalence of...Ch. 3 - Estimates of the prevalence of Alzheimers disease...Ch. 3 - Estimates of the prevalence of Alzheimers disease...Ch. 3 - Estimates of the prevalence of Alzheimers disease...Ch. 3 - Estimates of the prevalence of Alzheimers disease...Ch. 3 - Estimates of the prevalence of Alzheimers disease...Ch. 3 - Estimates of the prevalence of Alzheimers disease...Ch. 3 - Suppose a study of Alzheimers disease is proposed...Ch. 3 - Suppose a study of Alzheimers disease is proposed...Ch. 3 - Commonly used vaccines for influenza are trivalent...Ch. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Genetics Suppose that a disease is inherited via a...Ch. 3 - Genetics Suppose that a disease is inherited via a...Ch. 3 - Genetics Suppose that a disease is inherited via a...Ch. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Suppose that a disease is inherited via an...Ch. 3 - Suppose that a disease is inherited via an...Ch. 3 - Prob. 39PCh. 3 - Suppose that a disease is inherited via a...Ch. 3 - Suppose that a disease is inherited via a...Ch. 3 - Suppose that a disease is inherited via a...Ch. 3 - Suppose that a disease is inherited via a...Ch. 3 - Prob. 44PCh. 3 - Prob. 45PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48PCh. 3 - Prob. 49PCh. 3 - Obstetrics The following data are derived from the...Ch. 3 - Obstetrics The following data are derived from the...Ch. 3 - Obstetrics The following data are derived from the...Ch. 3 - Pulmonary Disease The familial aggregation of...Ch. 3 - Pulmonary Disease The familial aggregation of...Ch. 3 - Suppose, alternatively, that if the father is a...Ch. 3 - Suppose, alternatively, that if the father is a...Ch. 3 - Prob. 57PCh. 3 - The familial aggregation of respiratory disease is...Ch. 3 - The familial aggregation of respiratory disease is...Ch. 3 - The familial aggregation of respiratory disease is...Ch. 3 - The familial aggregation of respiratory disease is...Ch. 3 - Pulmonary Disease The familial aggregation of...Ch. 3 - Pulmonary Disease The familial aggregation of...Ch. 3 - Genetics, Obstetrics Precise quantification of...Ch. 3 - Precise quantification of smoking during pregnancy...Ch. 3 - Precise quantification of smoking during pregnancy...Ch. 3 - What is another name for this quantity? Suppose it...Ch. 3 - Research into cigarette-smoking habits, smoking...Ch. 3 - Research into cigarette-smoking habits, smoking...Ch. 3 - Research into cigarette-smoking habits, smoking...Ch. 3 - Research into cigarette-smoking habits, smoking...Ch. 3 - Research into cigarette-smoking habits, smoking...Ch. 3 - Research into cigarette-smoking habits, smoking...Ch. 3 - Pulmonary Disease Research into cigarette-smoking...Ch. 3 - Pulmonary Disease Research into cigarette-smoking...Ch. 3 - Laboratory measures of cardiovascular reactivity...Ch. 3 - Laboratory measures of cardiovascular reactivity...Ch. 3 - Laboratory measures of cardiovascular reactivity...Ch. 3 - The data set in Table 3.12 is based on 214...Ch. 3 - The data set in Table 3.12 is based on 214...Ch. 3 - The data set in Table 3.12 is based on 214...Ch. 3 - A drug company is developing a new pregnancy-test...Ch. 3 - A drug company is developing a new pregnancy-test...Ch. 3 - A drug company is developing a new pregnancy-test...Ch. 3 - Gynecology A drug company is developing a new...Ch. 3 - The Chinese Mini-Mental Status Test (CMMS)...Ch. 3 - The Chinese Mini-Mental Status Test (CMMS)...Ch. 3 - Mental Health The Chinese Mini-Mental Status Test...Ch. 3 - Construct an ROC curve based on the table...Ch. 3 - Mental Health The Chinese Mini-Mental Status Test...Ch. 3 - Calculate the area under the ROC curve. Interpret...Ch. 3 - Demography A study based on data collected from...Ch. 3 - Prob. 94PCh. 3 - Demography A study based on data collected from...Ch. 3 - Demography A study based on data collected from...Ch. 3 - Prob. 97PCh. 3 - The 4 allele of the gene encoding apolipoprotein E...Ch. 3 - Mental Health The 4 allele of the gene encoding...Ch. 3 - Mental Health The 4 allele of the gene encoding...Ch. 3 - Cardiovascular Disease A fascinating subject of...Ch. 3 - Cardiovascular Disease A fascinating subject of...Ch. 3 - Are these proportions prevalence rates, incidence...Ch. 3 - Prob. 104PCh. 3 - A dominantly inherited genetic disease is...Ch. 3 - A dominantly inherited genetic disease is...Ch. 3 - Prob. 107PCh. 3 - Infectious Disease, Cardiovascular Disease A...Ch. 3 - Infectious Disease, Cardiovascular Disease A...Ch. 3 - Infectious Disease, Cardiovascular Disease A...Ch. 3 - Prob. 114PCh. 3 - Genetics Suppose a birth defect has a recessive...Ch. 3 - A further study finds that after 10 generations...Ch. 3 - A further study finds that after 10 generations...Ch. 3 - Orthopedics Piriformis syndrome is a pelvic...Ch. 3 - Prob. 119PCh. 3 - Orthopedics Piriformis syndrome is a pelvic...Ch. 3 - Prob. 121PCh. 3 - Cancer Breast cancer is considered largely a...Ch. 3 - Cancer Breast cancer is considered largely a...Ch. 3 - Cancer Breast cancer is considered largely a...Ch. 3 - Prob. 125PCh. 3 - Cardiovascular Disease Mayo Clinic investigators...Ch. 3 - Prob. 127PCh. 3 - Prob. 128PCh. 3 - Prob. 129PCh. 3 - Prob. 130PCh. 3 - Prob. 131PCh. 3 - Prob. 132PCh. 3 - Radiology Mobile displays have the potential to...Ch. 3 - Radiology Mobile displays have the potential to...Ch. 3 - Prob. 135PCh. 3 - Prob. 136PCh. 3 - Prob. 137PCh. 3 - Cardiovascular Disease The ankle-arm...Ch. 3 - Cardiovascular Disease The ankle-arm...Ch. 3 - Cardiovascular Disease The ankle-arm...Ch. 3 - Prob. 141PCh. 3 - Prob. 142PCh. 3 - Prob. 143PCh. 3 - Obstetrics, Health Promotion A study was performed...
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