Mental health in America. In the Mental Health Surveillance Study, clinicians interviewed a very large random sample of American adults so as to diagnose the presence of mental disorders in the prior 12 months. There are many types of mental disorders, and a person can suffer from more than one. Let X represent the number of mental disorders a person has experienced in the past year. Based on this study, we can assign the following probability distribution to X in the American adult population: X 0 1 2 3 4 or more
P(X) 0.775 0.149 0.041 0.022 0.013
(a) Explain why this is a valid probability distribution. Is the sample space discrete orcontinuous?
(b) Find P(X <2) and P(1≤X≤3).
(c) Obtain the probability that a randomly selected American adult suffers from
(i) at least one mental disorder
(ii) either one or two mental disorders