Answer appropriately

1. Consider a Markov chain X, with the state space as non-negative integers and transition function: 1/2 if x = y 1/2 if x > 0 and y = x - 1 P(x, y) = (1/2) #+1 if x = 0 and y > 0 O otherwise (a) Calculate Pno. Hint: Use induction upon n. (b) If this Markov chain recurrent or transient? Prove your answer.\fQuestion 27 1 pts Which one of the following statements is correct: Unbiased estimators are always asymptotically unbiased Asymptotically unbiased estimators are always unbiased O Asymptotically unbiased estimators are always consistent Unbiased estimators are always consistent