Discuss the below problem:
Q: Suppose that infants are classified as low birth weight if they have birth weight ≤2500g, and as normal birth weight if have birth weight ≥2501g. Suppose that infants are also classified by length of gestation in the following four categories: <20 weeks, 20-27 weeks, 28-36 weeks, >36 weeks. Assume the probabilities of the different period of gestation are as given in the table below:
Distribution of length of gestation
|
Length of gestation
|
Probability
|
|
<20 weeks
|
.0004
|
|
20-27 weeks
|
.0063
|
|
28-36 weeks
|
.0848
|
|
>36 weeks
|
.9085
|
Also assume that the probability of low birth weight given that length of gestation is <20 weeks is .540, the probability of low birth weight given that length of gestation is 20-27 weeks is .813, the probability of low birth weight given that length of gestation is 28-36 weeks is .378, and the probability of low birth weight given that length of gestation is >36 weeks is .031.
a) What is the probability of having a low birth weight infant?
b) Show that the events {length of gestation ≤ 27 weeks} and {low birth weight} are not independent.