14.12 Consider a simple random walk with p = 1/2 started from S0 = 0, and let T = inf{n N | Sn =

14.12 Consider a simple random walk with p = 1/2 started from S0 = 0, and let Tα = inf{n ∈ N | Sn = α or Sn = −α}, the first time the random walk exits from (−α, α), or equivalently first hitting time of

(−∞, α]∪[α,∞). Using the methodology presented in the examples, find an estimate for the expected value of Tα and for the moment generating function of Tα.