Probability density function Watch

superkillball
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#1
Report Thread starter 12 years ago
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I got stuck on the question below.
K(1+x)^(alpha) >=0
(1+x)^(alpha)>=0
(alpha) ln (1+x) >= ln 0

ln 0 doesnt exist. I can't figure out the range.
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Jonny W
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Report 12 years ago
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For any a, (1 + x)^a >= 0 for all x > 0. So you don't have to worry about the pdf being negative.

f can be made into a pdf iff (int from 0 to infinity) (1 + x)^a dx is finite, which is true iff a < -1.

If a < -1 then

(int from 0 to infinity) (1 + x)^a dx
= [ (1 + x)^(a + 1)/(a + 1) ] (from 0 to infinity)
= -1/(a + 1)

and K = -(a + 1).
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