Patients who have artificial hip-replacement surgery experience pain the first day after surgery. Typically, the pain is measured on a subjective scale using values of 1 to 5. Let x represent the random variable, the pain score as determined by the patient. The probability distribution for x is believed to be as below. (Give your answers correct to two decimal places.)
x 1 2 3 4 5
P(x) 0.12 0.16 0.23 0.20 0.29
(a) Find the mean of x.
(b) Find the standard deviation of x.