Example 3.12

Suppose we are conducting a hypertension-screening program

in the home. Consider all possible pairs of DBP measurements of the mother

and father within a given family, assuming that the mother and father are not

genetically related. This sample space consists of all pairs of numbers of the form

(X, Y) where X > 0, Y > 0. Certain specific events might be of interest in this context.

In particular, we might be interested in whether the mother or father is hypertensive,

which is described, respectively, by events A = {mother's DBP 90}, B = {father's DBP

90}. These events are diagrammed in Figure 3.4.

Suppose we know that Pr(A) = .1, Pr(B) = .2. What can we say about Pr(A B) =

Pr(mother's DBP 90 and father's DBP 90) = Pr(both mother and father are

hypertensive)? We can say nothing unless we are willing to make certain

assumptions.

Let X be the random variable representing the number of hypertensive adults in Example 3.12. What is its cumulative distribution function?