Question: You throw darts at a board with 20 equally likely spaces. You throw until you hit 1, then you throw until you hit 2, then

You throw darts at a board with 20 equally likely spaces. You throw until you hit "1," then you throw until you hit "2," then you throw until you hit "3," etc., and finally you throw until you hit "20." Let X be the number of throws you make to achieve this goal.
a. What are the expected value and standard deviation of X?
b. Let Y be the number of throws needed until the 20th time hitting 1. Do X and Y have the same distribution? Why or why not?

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