Page 372 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV 2- izkf;drk dh vuqHkfod vFkok lkaf[;dh; fopkjèkkjk (Empirical statistical Approach of Probability)
3- izkf;drk dh vkRepsruk vFkok fo"k;xr fopkjèkkjk (Personalistic of Subjective Approach of
Probability)
4- izkf;drk dh lwfDr lacaèkh vFkok vkèkqfud fopkjèkkjk (Axiomatic or Morden Approach to
Probability)
1- izkf;drk dh ijaijkoknh vFkok xf.krh; fopkjèkkjk
(Classical or Mathematical Approach of Probability)

izkf;drk osQ vFkZ ,oa ekiu osQ lacaèk esa ;g lcls ljy vkSj izkphu fopkjèkkjk gS vkSj bl vkèkkj ij fudkyh
xbZ izkf;drk dks roZQiw.kZ ;k Lo;afl¼ izkf;drk Hkh dgrs gSaA Laplace us fy[kk gS fdμ¶vuqowQy ?kVukvksa dk
leku lEHkkouk okyh lEiw.kZ ?kVukvksa osQ lkFk vuqikr gh izkf;drk gSA¸

?kVuk ?kVus dh izkf;drk =

Example: ,d FkSys esa 4 yky rFkk 5 lisQn xsan gS rks FkSys esa ls ,d xsan fudkyus dh n'kk esa mlosQ yky gksus
dh izkf;drk 4/9 gksxhA D;ksafd vuqowQy ifjfLFkfr;ksa dh la[;k 4 gS rFkk oqQy lEHkkfor ifjfLFkfr;k¡ (FkSys esa
lHkh xsnksa dh la[;k) 9 gSA
ijEijkoknh fopkjèkkjk osQ vkèkkj ij xf.krh; :i esa izkf;drk dh xf.krh; ifjHkk"kk Hkh nh tkrh gSA mlosQ
vuqlkj ;fn dksbZ ?kVuk m ckj gks ldrh gS vkSj n ckj ugh gks ldrh rFkk lHkh ?kVuk leku :i ls ?kfVr gksus
m n
okyh gS rks ?kVuk osQ ?kVus dh izkf;drk p = rFkk ?kVuk u gksus dh izkf;drk q = A ;g è;ku
m + n m + n
jgs fd p + q = 1 vFkkZr p = 1 – q vFkok q = 1 – p gksrk gSA
Example: ,d iklk isQdus ij mlosQ Åijh Hkkx ij 3 ;k 4 dk vad vkus dh izkf;drk Kkr djuh gS rks 3

;k 4 nks ?kVuk;s gS] ftUgsa m dgk tk;sxkA blosQ vfrfjDr 1, 2, 5 vkSj 6 vFkkZr ?kVuk;sa gS ftUgsa n dgsaxsA bl
2 2 1
vkèkkj ij 3 ;k 4 vad vkus dh izkf;drk = = = A
2 + 4 6 3

2- izkf;drk dh vuqHkkfod vFkok lkaf[;dh; fopkjèkkjk
(Empirical or Statistical Approach of Probability)
izkf;drk dh bl fopkjèkkjk osQ vkèkkj ij x.kuk dh xbZ fd izkf;drk dks ¶lkis{k vko`fÙk izkf;drk¸ (Relaive
Exequency Probability) vFkok mÙkjorhZ izkf;drk (Posterior Probability) Hkh dgrs gSaA
bl fopkjèkkjk osQ vkèkkj ij miyCèk leadksa ;k vko`fÙk;ksa vFkok vuqHkoks osQ vkèkkj ij izkf;drk dh x.kuk dh
tkrh gSA
Example: fiNys o"kZ osQ vk¡dM+ksa esa ik;k x;k fd yxHkx 10% mRikn ?kfV;k fdLe dk curk gSA pkyw o"kZ esa
500 oLrqvksa dk mRiknu gksuk gS rks fiNys leadksa osQ vkèkkj ij ;g dgk tk ldrk gS fd 500 × 10/100 =
50% oLrq;sa ?kfV;k fdLe dh gksxhA

bl fopkjèkkjk osQ vuqlkj ljy lw=k esa izkf;drk dh x.kuk dks fuEu izdkj ls j[kk tk ldrk gSμ
r
p =
n
r = Relative frequency
n = Number of items
Example: ,d e'khu }kjk cuk;s x;s 1000 mRiknksa esa 40 ?kfV;k fdLe osQ gS rks ?kfV;k fdLe osQ leku dh

366 LOVELY PROFESSIONAL UNIVERSITY