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Introducton
Inballisticlaboratoryresearchthetoolwhichenablestoassessobjectivelyand
veryprobablytheparameterdistributionofchosencharacteristicsofpopulation
elementsisthetheoryofmeasurementuncertaintyinvolvingelementarylawsof
probabilitycalculusandmathematicalstatistics.Thatiswhyintheinitialpartof
thepresentworkonlyessentialselectiveinformationwasdiscussed9relatingto
probabilitycalculusandmathematicalstatistics9suchasunidimensionalrandom
variables9multidimensionalrandomvariables9distributionparametersofacho-
sencharacteristicamongpopulationelements9expectedvalue9single-pointand
intervalestimation9aswellasthePearsonlinearcorrelationcoefficient.Thecru-
cialpartofthepresentworkisthediscussionofstatisticaldistributions.Thestati-
sticaldistributionwhichhasbeendiscussedindetailisasingle-pointdistribution.
Thiswasduetothefactthatthisdistributionisessentialfordefiningmulti-point
distributionswhich9basically9areamulti-compositionofasingle-pointdistri-
bution.Asingle-pointdistributionwaspresentedasthedegenerationofaconti-
nuousuniformdistributiontoasinglepoint.Further9asingle-pointdistribution
wastransformedintoann-pointdistribution9otherwiseknownastheBernoulli
binominaldistribution.ApplyingtherandomvariableoftheBernoullibinominal
distribution9satisfyingthecondition
EX
[
k
()
ω
]
±
np
±
X
±
const9
beingthePois-
sontheoremforverylowvaluesofprobabilitypofasuccessandagreatnumber
ofhighvaluepointsn9afunctionwasderived9thatofthePoissondistribution
ofprobability9constitutingthelimitdistributionforBernoulli’sdistribution.The
deMoivre-Laplacetheoremwasalsoquoted9relatingtoBernoulli’sbinominal
distribution9whichshowsthatinthebordercrossingforthisdistributionitcoinci-
deswithGaussiannormaldistribution9whichdistributioncanbeappliedtoalmost
allprocessestakingplaceinnatureandmanyotherwalksoflife.Achisquare
distribution
()
X
2
wasalsodiscussedforrandomvariable
Y
k
9
beingthesumof
squareskofindependentrandomvariablesofGaussiannormaldistribution.The
lastrandomdistributiondiscussedisStudent’st-distributionusedinassessing
measurementuncertaintytoestimatetheconfidenceintervalandconfidencelevel
offindingthereinthedistributionparameterofarithmeticalaverageofpopulation
randomvariableiftherandomsampledoesnotexceed30measurements(n<30).
9
