Page 387 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—27% izkf;drk dk ;ksxkRed ,oa xq.kkRed fu;e

fd ,d ckj ,d ?kVuk ?kfVr gksus ij gh nwljh ?kVuk ?kVsxh] lizfrcUèk izkf;drk dgykrh gSA mnkgj.k uksV
osQ fy,] rk'k dh xM~Mh esa ,d iÙkk fudkyus osQ ckn ;fn mls iqu% okil u j[kk tk, rks nwljh ckj
yky ;k dkys jax osQ iÙks fudy vkus dh izkf;drk igyh ckj osQ ifj.kke ij fuHkZj gksxhA ;fn igyh
ckj yky ;k dkyk iÙkk fudyrk gS vkSj mls okil xM~Mh esa ugha j[kk tkrk rks nwljh ckj yky jax ;k
26
dkys jax osQ iÙks osQ fudyus dh izkf;drk gksxhA ;fn A o B nks vkfJr ?kVuk,¡ gksa rks muosQ ,d
51
lkFk ?kVus dh izkf;drk igyh ?kVuk osQ gksus dh izkf;drk vkSj nwljh ?kVuk osQ ml fLFkfr esa gksus dh
izkf;drk tcfd igyh gks pqoQh gS bu nksuksa dk xq.kuiQy gSA
P(A and B) = P(A) × P(B/A)
P(AB) = P(B) × P(A/B)
tgk¡ P(B/A) B dh lizfrcUèk izkf;drk gS (vFkkZr~ A ?kfVr gks pqdh gS) ,oa P(A/B) A dh lizfrcUèk
izkf;drk gSA (vFkkZr~ B igys ?kfVr gks pqdh gSA)
izek.k (Proof)μeku yhft, A osQ ?kVus osQ voljksa dh oqQy la[;k (pkgs B ?kVs ;k u ?kVs) m + m 2
1
gS ftuesa ls m ,slh ifjfLFkfr;k¡ gSa ftuesa A o B lkFk&lkFk ?kVrh gSaμ
1
m m / n P(AB)
P(B/A) = 1 = 1 =
m + m 2 ( m + m ) / n P(A)
1
2
1
P(AB) = P(A) × P(B/A)
P(AB) PA ∩( B)
blh izdkj P(A/B) = =
P(B) P(B)
P(AB) = P(B) × P(A/B)
rhu ?kVukvksa A, B o C osQ fy,μ
P(ABC) =P(A) × P(B/A) × P(C/AB)
tgk¡ P(C/AB) = C osQ ?kVus dh izkf;drk tcfd A o B ?kVuk,¡ ?kfVr gks xbZ gSaA
mnkgj.k (Illustration 8) : ;fn ,d rk'k dh xM~Mh ls rhu iÙks ,d osQ ckn ,d fcuk fiNys iÙks dks
okil j[ks fudkys tk,a rks muosQ ckn'kkg] csxe o bDdk osQ blh Øe esa vkus dh izkf;drk Kkr dhft,A
4
gy (Solution) : ,d ckn'kkg osQ fudkys tkus dh izkf;drk =
52
4
,d csxe osQ fudyus dh izkf;drk ckn'kkg fudyus osQ ckn =
51
xqyke osQ fudyus dh izkf;drk tcfd ,d ckn'kkg o ,d csxe fudy pqdh gks
4
=
50
;s vkfJr ?kVuk,¡ gSa vr% feJ izkf;drk
4 4 4 64 8
= × × = =
52 51 50 132600 16575
mngj.k (Illustration 9) : ,d FkSys esa 14 xsansa gSa ftuesa 6 yky] 3 ihyh o 5 dkyh gSaA rhu xssansa fcuk
okil j[ks ,d osQ ckn ,d fudkyh tkrh gSaA D;k izkf;drk gS fd os yky] ihyh rFkk dkyh blh Øe
esa gksaxh\
gy (Solution) : oqQy 14 xsanksaa esa ls rhu xsansa ,d fuf'pr Øe esa fudkyuh gSaμigyh] yky] nwljh ihyh

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