The following data are derived from the Monthly Vital Statistics Report (October 1999) issued by the National Center for Health Statistics [10]. These data are pertinent to livebirths only. Suppose that infants are classified as low birthweight if they have a birthweight <2500 g and as normal birthweight if they have a birthweight ≥2500 g. Suppose that infants are also classified by length of gestation in the following five categories: <28 weeks, 28–31 weeks, 32–35 weeks, 36 weeks, and ≥37 weeks. Assume the probabilities of the different periods of gestation are as given in Table 3.8. Also assume that the probability of low birthweight is .949 given a gestation of <28 weeks, .702 given a gestation of 28–31 weeks, .434 given a gestation of 32–35 weeks, .201 given a gestation of 36 weeks, and .029 given a gestation of ≥37 weeks., 1 What is the probability of having a low birthweight infant? 2 Show that the events {length of gestation ≤ 31 weeks} and {low birthweight} are not independent. 3 What is the probability of having a length of gestation ≤36 eeks given that an infant is low birthweight?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Obstetrics
The following data are derived from the Monthly Vital Statistics Report (October 1999) issued by the National Center for Health Statistics [10]. These data are pertinent to livebirths only.
Suppose that infants are classified as low birthweight if they have a birthweight <2500 g and as normal birthweight if they have a birthweight ≥2500 g. Suppose that infants are also classified by length of gestation in the following five categories: <28 weeks, 28–31 weeks, 32–35 weeks, 36 weeks, and ≥37 weeks. Assume the probabilities of the different periods of gestation are as given in Table 3.8. Also assume that the probability of low birthweight is .949 given a gestation of <28 weeks, .702 given a gestation of 28–31 weeks, .434 given a gestation of 32–35 weeks, .201 given a gestation of 36 weeks, and .029 given a gestation of ≥37 weeks.,
1 What is the probability of having a low birthweight infant?
2 Show that the
3 What is the probability of having a length of gestation ≤36 eeks given that an infant is low birthweight?
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