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Unformatted text preview: X denote the number of heads ²ipped. Then the pmf of X is p ( k ) = ( n k ) (1 / 10) k (9 / 10) n-k . Show which value of k this maximizes this. Hint: Look at the ratio: p ( k ) /p ( k + 1). When k is small, this is less than one, when k is large, this is bigger than one. ±ind the value of k when p ( k ) /p ( k + 1) ≈ 1. Why does this work? 5. (1.6.3) Cast a die a number of independent times until a six appears on the up side of the die. (a) ±ind the pmf p ( x ) of X , the number of casts needed to obtain that Frst six. (b) Show that ∑ ∞ x =1 p ( x ) = 1. (c) Determine P ( X = 1 , 3 , 5 , 7 ,... ) . (d) ±ind the cdf F X ( x ) = P ( X ≤ x ). 1...
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This note was uploaded on 10/26/2010 for the course MATHCS Math 316 taught by Professor Dr.paulhorn during the Fall '10 term at Emory.
- Fall '10