A principal value of 200 is invested for one year:

(i) The return rate over the year is estimated to be increasing linearly

from0.10to0.14.Inthiscaset =0.04t+0.1.Findthecumulativeinterest rate, rate function, future value.

(ii) The mean of the financial rate is defined by the integrable function u =0.04u+0.10 while the variance is u =0.002(1+0.001u).

Find the expectation of rate function and the expected future value.