1. We havekcoins. The probability of Heads is the same for each coin and is a random variableQthat is uniformly distributed on [0,1]. We assume that conditioned onQ=q, all coin tosses are independent. Fori= 1,2, . . . , k, letTibe the number of tosses of theithcoin until the toss results in Heads for the first time (including the toss that results in the first Heads). You may find the following integral useful: For any non-negative integerskandm,

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