Let τ be the random time when a random walk first hits either the point x = 2 or −2

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Let τ be the random time when a random walk first hits either the point x = 2 or −2. That is :
τ = τ1 = min {n : |Sn| = 2}
Please find the probability distribution and the expected value of τ. Hint: You can consider consecutive
pairs with a ’size of 2’ such as (1, 1),(−1, −1) and consecutive pairs such as (−1, 1),(1, −1) separately
and get help from first success probability. (You don’t have to of course, as long as you solve the question
any method is great.)