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# HW03 - STAT 36-217 HW 3 due Thursday 10:30 AM 1 Suppose...

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STAT 36-217, HW 3, due Thursday 09/17/2009, 10:30 AM 1. Suppose that we have n coins such that if the i th coin is flipped, heads will appear with probability i/n , i = 1 , 2 , . . . , n . When one of the coins is randomly selected and flipped, it shows heads. Find an expression (involving n and k ) for the probability that it was the k th coin (where 1 k n ) (you may need the fact that 1+2+ . . . + n = n ( n +1) / 2). 2. ( Three prisoners. ) Three prisoners, Antonio, Beppe and Carlo are on death row. The governor decides to pardon one of them, randomly chosen. He informs the warden of his choice but instructs him to keep the name of the pardoned prisoner secret. The next day, Antonio, who, incidentally, never took 36-217, tries to get the warden to tell him who had been pardoned. The warden refuses. Antonio then asks which of Beppe or Carlo will be executed. The warden thinks for a while and tries to remember what he had learned in 36-217, then tells Antonio that Beppe is to be executed.

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HW03 - STAT 36-217 HW 3 due Thursday 10:30 AM 1 Suppose...

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