The following table shows the cumulative distribution function for the random variable X, the number of persons seeking emergency room treatment unnecessarily per day in a small hospital.

x 0 1 2 3 4 5

F(x) 0.01 0.11 0.41 0.81 0.91 1

(a) Compute the following probabilities: (i) P(1 < X 4); (ii) P(X > 3).

(b) Compute the expected number of persons seeking emergency room treatment unnecessarily in a day.

(c) Compute the probability number of persons seeking emergency room treatment unnecessarily in a day is at most 2.

(d) Compute P(X ), where is the mean number of persons seeking emergency room treatment unnecessarily in a day.