Suppose that infants are classied as low birthweight if they have a birthweight

Question

Suppose that infants are classied as low birthweight if they have a birthweight < 2500g and as normal birthweight if they have a birthweight 2500g. Suppose that infants are also classied by length of gestation in the following ve categories: < 28 weeks, 28 31 weeks, 32 35 weeks, 36 weeks, and 37 weeks. Assume that the probabilities of the dierent periods of gestation are given in Table 3.8 (Distribution of length of gestation).

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.

(a). What is the probability of having a low birthweight infant?

(b). Show that the events{length of gestation 30 weeks}and{low birthweight} are NOT independent.

Explanation / Answer

a)P(low birthweight)=P(<28 weeks)*P(low birthweight|<28 weeks)+P(28-31 weeks)*P(low birthweight|28-31 weeks)+P(32-35 weeks)*P(low birthweight|32-35 weeks)+P(36 weeks)*P(low birthweight|36 weeks)+P(>=37 weeks)*P(low birthweight|>=37 weeks)

=0.007*0.949+0.012*0.702+0.05*0.434+0.037*0.201+0.893*0.029=0.0701

b)

here as P(low birth weight) is different for different length of gestation and therefore it depends on period of gestation and hence depednent of length of gestation

c)

P(<=36|low birthweight)=1-P(>=37 weeks|low birthweight)

=1-P(>=37 weeks)*P(low birthweight|>=37 weeks)/P(low birthweight)

=1-0.893*0.029/0.0701 =0.6306

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