May I ask that how to do (ci),(cii),(d)

2 / 3 100% + H Mary is a nurse and is organizing the patients' visiting records for a physiotherapist, Jim. For those patients who have seen Jim on October 1, the number of treatments in the previous month (X) have been checked. Below is the corresponding probability distribution function: X 0 2 3 4 UI 6 P(X = x) 0.2 0.2 0.4 0. 15 0 0 0.03 k (a) Find the value of k. (b) Calculate the E(X) and o(X). Page 2 Assume every treatment charges $M. Use Y to represent the total treatment expenses for the above patient in the previous month. (ci) Currently M = 300, find E(Y) and Var( Y). (cii) Jim plans to change the treatment charges to a new level. To set E(Y) - $700. what should be the value of M? (Round off the answer to the nearest integer) (d) There are 8 appointments from 2:00 pm to 4:00 pm. Use the above information as reference, out of the 8 appointed patients, what is the probability that at least 3 of them had more than 2 treatments in the previous month