Expected steps to first reach a level

MediumProbability Stochastic Processes~4m

A walk starts at $0$ and each step moves $+1$ with probability $0.55$ or $-1$ with probability $0.45$ , independently. On average, how many steps does it take to reach position $+3$ for the first time?

Show hints (2)+

Positive drift $\Rightarrow$ the target is reached w.p. 1; use Wald's identity.
$E[S_T]=E[\text{step}]\cdot E[T]$ with $E[\text{step}]=0.1$ and $S_T=3$ .

Answer

Reveal answer →

30 (± 0.001)

Create a free account to see the full worked solution and track your progress.

Create a free account

Interview format: Trading Aptitude Tests, Betting Game Rounds

Expected steps to first reach a level

Answer

Related questions