UDC 519.2
ACCURATE ESTIMATES OF THE PROBABILITY OF A NON-NEGATIVE UNIMODAL
RANDOM VALUE INTO SPECIAL INTERVALS WITH INCOMPLETE INFORMATION
Abstract. Exact lower estimations are found for the probability that non-negative unimodal
random variable
μ
gets in the intervals
(m − ασμ ,
m + ασμ )
where the mode
m coincides with fixed first moment of random variable
μ,
σμ
is standard deviation and
m < σμ.
The parameter α
satisfies the inequalities
0 < α < m / σμ < 1.
The results of this study may be useful
in evaluating the probability of hitting the projectile zone when aimed shooting.
Keywords: linear functionals of unimodal distribution functions, extremal values, transformation of Johnson–Rogers,
exact generalized Chebyshoff inequalities for linear functionals of unimodal distribution functions.
FULL TEXT
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