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GeoMatt22
GeoMatt22
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The binomial distribution tends to be roughly symmetric (for large $n$ it is approximately normal). 

Since the ratio must be between 0 and 1, the uncertainty will be constrained by these bounds. Unless the mean ratio is exactly in the middle, one of these bounds will be more limiting than the other.

For a symmetric unimodal bell curve centered at $p$ to fit into the unit interval, its half-width must be less than $\min[\,p\,,1-p\,]$.

The binomial distribution tends to be roughly symmetric. Since the ratio must be between 0 and 1, the uncertainty will be constrained by these bounds. Unless the mean ratio is exactly in the middle, one of these bounds will be more limiting than the other.

The binomial distribution tends to be roughly symmetric (for large $n$ it is approximately normal). 

Since the ratio must be between 0 and 1, the uncertainty will be constrained by these bounds. Unless the mean ratio is exactly in the middle, one of these bounds will be more limiting than the other.

For a symmetric unimodal bell curve centered at $p$ to fit into the unit interval, its half-width must be less than $\min[\,p\,,1-p\,]$.

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GeoMatt22
GeoMatt22
  • 13.1k
  • 3
  • 39
  • 72

The binomial distribution tends to be roughly symmetric. Since the ratio must be between 0 and 1, the uncertainty will be constrained by these bounds. Unless the mean ratio is exactly in the middle, one of these bounds will be more limiting than the other.