Question: 8. (Pattern Appearance) Suppose that random digits are generated from the set {0, 1, . . . , 9} independently and successively. Find the expected

8. (Pattern Appearance) Suppose that random digits are generated from the set {0, 1, . . . , 9} independently and successively. Find the expected number of digits to be generated until the pattern

(a) 007 appears,

(b) 156156 appears,

(c) 575757 appears

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