9. Amber has decided to ask randomly selected people what their birthdays are until she has met people with birthdays on each and every day of the year. Ignoring February 29, find the expected value and the standard deviation of the number of people that Amber will need to meet in order to achieve her goal.

Hint: Let X1 = 1 for counting the first person that Amber will meet. Let X2 be the number of people Amber will meet until she finds a person whose birthday is different from the birthday of the first person she met. Let X3 be the number of people Amber will meet until she finds a person whose birthday is different from the first two birthdays that she has already recorded, and so on. Clearly, X, the number of people that Amber will need to meet in order to achieve her goal, satisfies the following equation.

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X = X+X2+X3+...+X365.