Stat447F08HW6Sol

Stat447F08HW6Sol - Prepared by Chuanlong Du Oct 22,2008 1....

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Unformatted text preview: Prepared by Chuanlong Du Oct 22,2008 1. Ex5.34 From Theorem 5.4 in the text book we know that the moment generating function of the binomial distribution is ? ? = 1 + ? ? 1 ? lim ? , ? = ? ? = lim ? , ? = 1 + ? ? 1 ? = lim ? , ? = 1 + ? ? ? 1 ? ? = lim ? 1 + ? ? 1 ? ? = ? ? ? 1 which is the moment generating function of the Poisson distribution. 2. Ex5.62 The negative binomial random variable is the number of trials on which the ?? success occurs, and the geometric random variable is the number of trials on which the 1 st success occurs. Thus we know that a geometric distribution with parameter is the negative binomial distribution with parameters 1 and . So we have ; = ; 1, = 1 1; , (b) Refer to Table one, we find that 1; 6, 0.3 = 0.3025 . So we know that 6; 0.3 = 1 6 1; 6, 0.3 = 1 6 0.3025 = 0.0504 3. Ex5.67 (a) ? = 12 200 = 0.06 > 0.05 , not satisfied (b) ?...
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Stat447F08HW6Sol - Prepared by Chuanlong Du Oct 22,2008 1....

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