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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
12
votes
A normal distribution inequality
Yes, the conjectured lower bound is true and can be proved using fairly simple, if somewhat tedious, analysis of derivatives.
First define
$$
b := f - N^2 = x(xN + n) - (xN + n)^2 + N(1-N)\>.
$$
The …