Yahoo Answers: Answers and Comments for Tricky problem in statistics... Help please... 10 Point reward!? [Mathematics]
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From Adam S
enCA
Sat, 06 Mar 2010 15:36:38 +0000
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Yahoo Answers: Answers and Comments for Tricky problem in statistics... Help please... 10 Point reward!? [Mathematics]
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https://ca.answers.yahoo.com/question/index?qid=20100306153638AAoRx5I
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From Paula: Each individual random number has a 1/k chance...
https://ca.answers.yahoo.com/question/index?qid=20100306153638AAoRx5I
https://ca.answers.yahoo.com/question/index?qid=20100306153638AAoRx5I
Sun, 07 Mar 2010 17:45:58 +0000
Each individual random number has a 1/k chance of falling in subinterval 1. So the distribution of X1 follows a binomial distribution:
p(X1 = i) = C(n, i) * (1/k)^i * (11/k)^(ni)
Where C(n,i) = n! / (i! * (ni)!), and * denotes multiplication.
A binomial distribution has mean np and variance np(1p). In this case p = 1/k, so:
mean(X1) = n/k
variance(X1) = n/k * (1  1/k) = n/k * (k1)/k
If we scale by 1/n (from X1 to Y1), then the mean scales by 1/n and the variance scales by 1/n^2, so:
mean(Y1) = 1/k
variance(Y1) = 1/nk * (k1)/k
(And standard deviation is square root of variance).