(a) Calculate the E(X) from p.d.f. f (x).(5分)

3. A survey found that the average hotel room rate in Taipei is $88.42 and the average room rate in Chiayi is $80.61. Assume that the data were obtained from two samples of 50 hotels each and that the standard deviations of the populations are $5.62 and $4.83, respectively. At α = 0.05, can it be concluded that there is a significant difference in the rates?(10分)