We have b = 18 × 109 bits that need to be sent over a channel which has a constant but random rate R bits/second with PMF: pR(r) = 1/3, if r = 3 × 109 bits/second 2/3, if r = 900 × 106 bits/second 0, otherwise.
Note that sending b bits at rate R bits/second takes T = g(R) = b/R seconds.
(a) What is the expected transmission rate E[R]?
(b) What is the expected transmission time E[T]?
(c) Based on your answers to (a) and (b), does E[g(R)] = g(E[R])?