Question

A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level.

Find the marginal distribution of blood pressure:

Answer 1

The marginal distribution of blood pressure is the sum of the probabilities across age groups for each blood pressure level. It provides the overall distribution of blood pressure irrespective of age.

Step-by-step explanation:

To find the marginal distribution of blood pressure, we sum the probabilities across age groups for each blood pressure level. Let's denote the blood pressure levels as
`\(BP_1, BP_2, \ldots, BP_n\),` and the age groups as
`\(Age_1, Age_2, \ldots, Age_m\)`. The marginal distribution
`\(P(BP_i)\)`for a specific blood pressure level
`\(BP_i\)`is calculated by adding the probabilities across all age groups for that particular blood pressure level:
`\(P(BP_i) = P(BP_i \cap Age_1) + P(BP_i \cap Age_2) + \ldots + P(BP_i \cap Age_m)\).`

This process is repeated for each blood pressure level, resulting in the complete marginal distribution of blood pressure. The marginal distribution provides a comprehensive view of the probability of each blood pressure level occurring, regardless of age. It is a useful measure for understanding the overall prevalence of different blood pressure categories within the employee population.

In conclusion, the marginal distribution of blood pressure condenses the information from the joint distribution of blood pressure and age groups. It simplifies the analysis by focusing on the probability of each blood pressure level, providing valuable insights for the company's health assessment program.