Let X₁, be the Markov chain with state space Z and transition probability P2,2+1 = P₁ P2,2-1 = 1- P₁ where p > 1/2. Assume X₁ = 0. (a) Let Y= min{Xo, X₁,...}. What is the distribution of Y? (b) For positive integer k, let T = why e(k) = ke(1). min{n: X₂ = k} and let e(k)= E[T]. Explain (c) Find e(1). Hint: part (b) might be helpful. (d) Use (c) to give another proof that e(1) = ∞o if p = 1/2.

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A: Referencehttps://www.investopedia.com/terms/e/expectedreturn.asp