(a) If you have a chance of getting each question right, what is the distribution of Q: the total number of questions you have to answer? (Give the name of the distribution and its parameters.) (b) Express the amount of money you win as a function of Q. (c) Find the expected amount of money you win.

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Chapter1: Combinatorial Analysis
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4. On a game show, you start with a prize pool of $1 000 000, but before you get it, you must
answer trivia questions. Every time you get a question wrong, the current prize pool is cut
in half, and you must keep answering questions. The game ends when you get a question
right and you receive whatever is left of the prize pool.
(For example, if you get the first two questions wrong, the prize pool is cut in half twice, so
it becomes $250 000. If you then get the third question right, you go home with $250 000 as
your winnings.)
(a) If you have a chance of getting each question right, what is the distribution of Q: the
total number of questions you have to answer? (Give the name of the distribution and
its parameters.)
(b) Express the amount of money you win as a function of Q.
(c) Find the expected amount of money you win.
Transcribed Image Text:4. On a game show, you start with a prize pool of $1 000 000, but before you get it, you must answer trivia questions. Every time you get a question wrong, the current prize pool is cut in half, and you must keep answering questions. The game ends when you get a question right and you receive whatever is left of the prize pool. (For example, if you get the first two questions wrong, the prize pool is cut in half twice, so it becomes $250 000. If you then get the third question right, you go home with $250 000 as your winnings.) (a) If you have a chance of getting each question right, what is the distribution of Q: the total number of questions you have to answer? (Give the name of the distribution and its parameters.) (b) Express the amount of money you win as a function of Q. (c) Find the expected amount of money you win.
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