answer all questions with explanation

Consider a simple random walk 3,, = 221:0 X,- be a simple random walk where Kg, 1' = 0,1... . are independent and identically distributed and have the following distribution: (a) Answer the following: (a) For a simple random walk with p = 0.3 and q = 0.31 with ab- sorbing barriers at 100 and 250 and starting at 150, determine the probability of absorbing to the barrier at 250 rst. (b) For an unrestricted simple random walk with p = 0.3 and q = 0.31 starting at 50, determine the probability that the walk will ever reach state 100 . (b) Do the following changes to the distribution of X.- still create a simple random walk? Justify your answer. (i) 2x; (ii) Xi