Question: A student rolls a die until the first 4 appears. Let X be the numbers of rolls required until (and including) this first 4. After

A student rolls a die until the first "4" appears. Let X be the numbers of rolls required until (and including) this first "4." After this is completed, he begins rolling again until he gets a "3." Let Y be the number of rolls, after the first "4," up to (and including) the next "3." E.g., if the sequence of rolls is 213662341261613 then X = 8 and Y = 7.
a. Find the expected value of X.
b. Find the expected value of Y.

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