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# hw2 - his/her family if you use method 2(c Which method...

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Mathematics 170A – HW2 – Due Tuesday, January 24, 2012. Problems 14,16,17,18,19,21,22,23 on pages 56-58. C. A community has m families with children. The largest family has k children. For i = 1 ,...,k , there are n i families with i children, so n 1 + n 2 + ··· + n k = m . Choose a child at random from the community in one of the following ways: 1. Choose one of the m families at random, and then choose one of the children at random from that family. 2. Choose one of the n 1 + 2 n 2 + ··· + kn k children at random. (a) What is the probability that the child chosen is the first-born in his/her family if you use method 1? (b) What is the probability that the child chosen is the first-born in
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Unformatted text preview: his/her family if you use method 2? (c) Which method results in the larger probability that the child chosen is the ±rst-born in his/her family? D. A coin has probability p of coming up heads and 1-p of coming up tails. Let x n be the probability that if the coin is tossed n times, the number of heads obtained is even. (a) Show that x n = p (1-x n-1 ) + (1-p ) x n-1 for n ≥ 1. (b) Let a n = 2 x n-1. Express a n in terms of a n-1 . (c) Use part (b) to compute a n , and therefore x n , for n ≥ 1. 1...
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