Consider a birth and death process with birth rates i = (i + 1),i 0, and death

Consider a birth and death process with birth rates λi = (i + 1)λ,i 0, and death rates μi = iμ,i 0.

(a) Determine the expected time to go from state 0 to state 4.

(b) Determine the expected time to go from state 2 to state 5.

(c) Determine the variances in parts

(a) and (b).