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chapter42601questions - ASSIGNMENT Chapter 4 Statistical...

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ASSIGNMENT Chapter 4 Statistical Methods NAME: Taehaeng,Lee 4.4 (6 points) Type of Random Variable . Identify the following random variables as discrete or continuous: a . The amount of flu vaccine in a syringe ANSWER Continuous Random variable b . The heart rate ( number of beats per minute ) of an American male ANSWER Discrete Random variable c . The time it takes a student to complete an examination ANSWER Continuous Random variable d . The barometric pressure at a given location ANSWER Continuous Random variable e . The number of registered voters who vote in a national election ANSWE Discrete Random variable f . You score on the SAT ANSWER Discrete Random variable 4.15 (3 points) A discrete random variable x can assume five possible values: 2,3,5,8, and 10. Its probability distribution is shown here:
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x p (x) 2 3 5 8 10 .15 .10 .25 .25 a . What is p (5) ? ANSWER 1- Other=0.25 P(5)= 0.25 b . What is the probability that x equals 2 or 10? ANSWER 0.15+.25= 0.4 c . What is P ( x 8)? ANSWER 0.75 4.22 (2 points) controlling the water hyacinth. Entomologists are continually searching for new biological agents to control the water hyacinth, one of the world’s worst aquatic weeds. an insect that naturally feeds on the water hyacinth is the delphacid. Female delphacids lay anywhere form one to four eggs onto a water hyacinth blade . The Annals of the Entomological Society of American (Jan. 2005) published a study of the life cycle of a South American delphacid species. The following table gives the percentages of water hyacinth blades that have one, two, three, and four delphacod eggs: One Egg Two Eggs Three eggs Four eggs Percentage of Blades 40 54 2 4 Source: Sosa, A.J., et al. “Life history of Megamelus scutellaris with decription of immature stages.” Annals of the Entomological Society of America, Vol. 98, No.1, 2005 (adaptes from Table 1). a . One of the water hyacinth blades in the study is randomly selected, and x , the number of delphacid eggs on the blade, is observed. Give the probability distribution of x . ANSWER X = x 1 2 3 4 P(X = x) 0.4 0.54 0.02 0.04 b . What is the probability that the blade has at least three delphacid eggs? ANSWER 0.02+0.04 = 0.06
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4.134 (5 points) Reliability of a bridge network . In the journal Networks (May 1995), a team of Chinese university professors investigated the reliability of several capacitates- flow networks. One network examined in the article and illustrated here is a bridge network with arcs a 1 , a 2 , a 3 , a 4 , a 5 , and a 6 . The probability distribution of the capacity x for each of the six arcs is provided in the following table: Arc Capacity x p (x) Arc Capacity x p (x) a 1 3 .60 2 .25 1 .10 0 .05 a 4 1 .90 0 .10 a 2 2 .60 1 .30 0 .10 a 5 1 .90 0 .10 a 3 1 .90 0 .10 a 6 2 .70 1 .25 0 .05 Source: Lin, J., et al. “On reliability evaluation of capacitated-flow network in terms of minimal pathsets.” Networks , Vol. 25, No. 3, May 1995, p.135 (Table 1) a 1 a 2
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chapter42601questions - ASSIGNMENT Chapter 4 Statistical...

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