EBK FUNDAMENTALS OF BIOSTATISTICS
8th Edition
ISBN: 9781305465510
Author: Rosner
Publisher: YUZU
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Chapter 4, Problem 57P
A study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of users who had ≤ 100 injections per month (light users) and 55% of users who had > 100 injections per month (heavy users) were HIV positive.
What is the
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30. An individual who has automobile insurance from a certain company is randomly selected. Let Y be the num- ber of moving violations for which the individual was cited during the last 3 years. The pmf of Y isy | 1 2 4 8 16p(y) | .05 .10 .35 .40 .10
a.Compute E(Y).b. Suppose an individual with Y violations incurs a surcharge of $100Y^2. Calculate the expected amount of the surcharge.
24. An insurance company offers its policyholders a num- ber of different premium payment options. For a ran- domly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows:
F(x)=0.00 : x < 10.30 : 1≤x<30.40 : 3≤ x < 40.45 : 4≤ x <60.60 : 6≤ x < 121.00 : 12≤ x
a. What is the pmf of X?b. Using just the cdf, compute P(3≤ X ≤6) and P(4≤ X).
Chapter 4 Solutions
EBK FUNDAMENTALS OF BIOSTATISTICS
Ch. 4.6 - What is the difference between a frequency...Ch. 4.6 - What is the difference between a probability-mass...Ch. 4.6 - In Table 4.4 the random variable X represents the...Ch. 4.7 - Suppose we select 3 students randomly out of a...Ch. 4.7 - Suppose we select 2 students randomly from a class...Ch. 4.9 - The probability of a woman developing breast...Ch. 4.9 - Suppose we have 10 subjects and the probability of...Ch. 4.13 - Suppose the number of motor-vehicle fatalities in...Ch. 4.13 - Suppose a rare infectious disease occurs at the...Ch. 4 - Let X be the random variable representing the...
Ch. 4 - Let X be the random variable representing the...Ch. 4 - Let X be the random variable representing the...Ch. 4 - Let X be the random variable representing the...Ch. 4 - Suppose we want to check the accuracy of...Ch. 4 - Suppose we want to check the accuracy of...Ch. 4 - Evaluate (100),(101),,(1010).Ch. 4 - Evaluate 9!.Ch. 4 - Suppose 6 of 15 students in a grade-school class...Ch. 4 - What is the expected number of students in the...Ch. 4 - What is the probability of obtaining exactly 6...Ch. 4 - What is the probability of obtaining at least 6...Ch. 4 - What is the expected value and variance for a...Ch. 4 - Prob. 14PCh. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Prob. 19PCh. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Suppose 10 gonorrhea cases are reported over a...Ch. 4 - Assume the number of episodes per year of otitis...Ch. 4 - Assume the number of episodes per year of otitis...Ch. 4 - An interesting question in pediatrics is whether...Ch. 4 - What is the probability that exactly 1 sibling...Ch. 4 - An interesting question in pediatrics is whether...Ch. 4 - What is the expected number of siblings in a...Ch. 4 - A national study found that treating people...Ch. 4 - A national study found that treating people...Ch. 4 - A national study found that treating people...Ch. 4 - The presence of bacteria in a urine sample...Ch. 4 - The presence of bacteria in a urine sample...Ch. 4 - The presence of bacteria in a urine sample...Ch. 4 - One interesting phenomenon of bacteriuria is that...Ch. 4 - One interesting phenomenon of bacteriuria is that...Ch. 4 - Otitis media is a disease that occurs frequently...Ch. 4 - Otitis media is a disease that occurs frequently...Ch. 4 - Otitis media is a disease that occurs frequently...Ch. 4 - Otitis media is a disease that occurs frequently...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An important issue in assessing nuclear energy is...Ch. 4 - Prob. 49PCh. 4 - An important issue in assessing nuclear energy is...Ch. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - A topic of some interest in the genetic literature...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - An article was published [13] concerning the...Ch. 4 - An article was published [13] concerning the...Ch. 4 - An article was published [13] concerning the...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - The number of legal induced abortions per year per...Ch. 4 - Table 4.19 Annual incidence of legal induced...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - Prob. 80PCh. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - The two-stage model of carcinogenesis is based on...Ch. 4 - The two-stage model of carcinogenesis is based on...Ch. 4 - The two-stage model of carcinogenesis is based on...Ch. 4 - The data in Table 4.20 were reported by men in the...Ch. 4 - The data in Table 4.20 were reported by men in the...Ch. 4 - Prob. 88PCh. 4 - Suppose the number of admissions to the emergency...Ch. 4 - Suppose the number of admissions to the emergency...Ch. 4 - Suppose the number of admissions to the emergency...Ch. 4 - Prob. 92PCh. 4 - Prob. 93PCh. 4 - Prob. 94PCh. 4 - Suppose a city is divided into eight census tracts...Ch. 4 - A study was performed concerning medical...Ch. 4 - Suppose the flight attendants total duration of...Ch. 4 - The more significant IFMs result in an aircraft...Ch. 4 - A study was performed to assess the feasibility of...Ch. 4 - A study was performed to assess the feasibility of...Ch. 4 - A clinical trial was conducted among 178 patients...Ch. 4 - Prob. 102PCh. 4 - Suppose we have 10 patients who receive...Ch. 4 - Mesothelioma is an asbestos-related neoplasm that...Ch. 4 - Mesothelioma is an asbestos-related neoplasm that...Ch. 4 - Mesothelioma is an asbestos-related neoplasm that...
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- 59. At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks.a. What is the probability that the next customer will request plus gas and fill the tank (A2 B)?b. What is the probability that the next customer fills the tank?c. If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?arrow_forward38. Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities .15, .35, .35, and .15, respectively. a. Calculate E(X) and then E(5 - X).b. Would the repair facility be better off charging a flat fee of $75 or else the amount $[150/(5 - X)]? [Note: It is not generally true that E(c/Y) = c/E(Y).]arrow_forward74. The proportions of blood phenotypes in the U.S. popula- tion are as follows:A B AB O .40 .11 .04 .45 Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? What is the probability that the phenotypes of two randomly selected individuals match?arrow_forward
- 53. A certain shop repairs both audio and video compo- nents. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A) = .6 and P(B) = .05. What is P(BA)?arrow_forward26. A certain system can experience three different types of defects. Let A;(i = 1,2,3) denote the event that the sys- tem has a defect of type i. Suppose thatP(A1) = .12 P(A) = .07 P(A) = .05P(A, U A2) = .13P(A, U A3) = .14P(A2 U A3) = .10P(A, A2 A3) = .011Rshelfa. What is the probability that the system does not havea type 1 defect?b. What is the probability that the system has both type 1 and type 2 defects?c. What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? d. What is the probability that the system has at most two of these defects?arrow_forwardThe following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)arrow_forward
- Please provide the solution for the attached image in detailed.arrow_forward20 km, because GISS Worksheet 10 Jesse runs a small business selling and delivering mealie meal to the spaza shops. He charges a fixed rate of R80, 00 for delivery and then R15, 50 for each packet of mealle meal he delivers. The table below helps him to calculate what to charge his customers. 10 20 30 40 50 Packets of mealie meal (m) Total costs in Rands 80 235 390 545 700 855 (c) 10.1. Define the following terms: 10.1.1. Independent Variables 10.1.2. Dependent Variables 10.2. 10.3. 10.4. 10.5. Determine the independent and dependent variables. Are the variables in this scenario discrete or continuous values? Explain What shape do you expect the graph to be? Why? Draw a graph on the graph provided to represent the information in the table above. TOTAL COST OF PACKETS OF MEALIE MEAL 900 800 700 600 COST (R) 500 400 300 200 100 0 10 20 30 40 60 NUMBER OF PACKETS OF MEALIE MEALarrow_forwardLet X be a random variable with support SX = {−3, 0.5, 3, −2.5, 3.5}. Part ofits probability mass function (PMF) is given bypX(−3) = 0.15, pX(−2.5) = 0.3, pX(3) = 0.2, pX(3.5) = 0.15.(a) Find pX(0.5).(b) Find the cumulative distribution function (CDF), FX(x), of X.1(c) Sketch the graph of FX(x).arrow_forward
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