1. To explore the establishment of a centralized appointment system for outpatients based on big data, the status of patients who applied for multiple examinations

(number of examination items 2) in a large hospital outpatient department in one day is investigated. For eight common examinations (e.g., computerized tomography and pathology), the probability distribution of the number of examination items for the patients (pmf) is shown in Table 4.8.

(a) Find the probability that the number of examination items for multiple examinations of a patient is less than six.

(b) Plot the cdf of the number of patient examination items for multiple examinations and describe its graphical characteristics.

(c) What is the difference between the pmf and cdf?

(d) Find the expected value, variance, and standard deviation of the number of patient examination items for multiple examinations.

(e) Describe the relationship between the probability distribution and relative frequency distribution.