Modified Random Walk: Expected Duration and Recurrence Equation Analysis

[Poirot1]

(1)Consider the expected duration of the modified random walk. Show that conditioning on the first step produces a recurrence equation of the following form.​

Ea = ˜pEa+1 + ˜qEa−1 + ˜c.
(2)Clearly identify the values of ˜p, ˜q and ˜c in terms of p, q and r.
Thanks

 

[CaptainBlack]

(1)Consider the expected duration of the modified random walk. Show that conditioning on the first step produces a recurrence equation of the following form.​

Ea = ˜pEa+1 + ˜qEa−1 + ˜c.
(2)Clearly identify the values of ˜p, ˜q and ˜c in terms of p, q and r.
Thanks

Please post the entire question, in particular the definition of your modified random walk

CB