Researchers investigating the SARS (severe acute respiratory syndrome) epidemic in Hong Kong in 2003 found that the probability distribution of the time from infection to onset of the disease could be described by ƒ(t) = 0.07599t^1.43e^-t/2.62 for t 7 0, where t is the time in days.

(a) Find the mean of this distribution. (When using a calculator to perform this integration, an upper limit of 40 may be used, since the probability that the time is greater than 40 days is extremely small.)
(b) Find the standard deviation.
(c) Find the probability that the time from infection to onset of the disease is between 5 and 10 days.