Page 385 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

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

= G 5 F 6 H + J − 4I F 5 ×G 4I J = 25 + 24 − 20 = 29 uksV
5K H
5K
30
30
30
6
27-2 izkf;drk dk xq.kkRed fu;e (Multiplicative Law of Probability)
tc nh xbZ lHkh LorU=k ?kVukvksa osQ ,d lkFk ?kVus dh izkf;drk Kkr djuh gks rc izkf;drk dh xq.kkRed
fu;e dk iz;ksx fd;k tkrk gSA xq.ku izes; nks ;k nks ls vf/d LorU=k ?kVukvksa osQ ,d lkFk ?kVus dh
izkf;drk muosQ vyx&vyx ?kfVr gksus dh O;fDrxr izkf;drkvksa dk xq.kuiQy gSA ;fn nks ?kVuk,¡ A o
B LorU=k gSa rks muosQ ,d lkFk ?kVus dh izkf;drk fuEu gksxhμ
P(A rFkk B) = P(A) × P(B)
leqPp; :i esa P(A ∩ B) = P(A) . P(B)

izek.k (Proof)μekuk ,d ?kVuk A oqQy n rjhdksa ls ?kV ldrh gS ftuesa ls a rjhosQ vuqowQy gS vkSj
1
1
?kVuk B oqQy n rjhdksa ls ?kV ldrh gS ftuesa ls a rjhosQ vuqowQy gSa] rcμ
2
2
a a
P(A) = 1 and P(B) = 2
n 1 n 2
;fn nksuksa ?kVuk,¡ ,d lkFk ?kVsa rks iz;ksxkuqlkj vuqowQy ifjfLFkfr;k¡ a × a gksaxh vkSj lEHkkO; ifjfLFkfr;k¡
1
2
n × n gksaxhA vr% A o B osQ lkFk ?kVus dh izkf;drkμ
1
2
a × a a a
P(A and B) = 1 2 = 1 × 2 = P(A) × P(B)
n × n 2 n 1 n 2
1
rhu LorU=k ?kVukvksa dk lw=kμP(A and B and C) = P(A) × P(B) × P(C)
rhu ls vf/d LorU=k ?kVukvksa dk lw=kμ
P(1, 2, 3, 4,......n) = P × P × P × P × ...... P n
4
3
1
2
nks ;k nks ls vf/d Lora=k ?kVukvksa osQ ,d lkFk dh izkf;drk muosQ vyx&vyx <ax ls
?kfVr gksus dh izkf;drkvksa dk xq.kuiQy gSA

mnkgj.k (Illustration 4) :

,d flDosQ dks rhu ckj mNkyus ij lHkh (3) iV vkus dh izkf;drk D;k gS\
gy Solution : flDosQ dks rhuksa ckj mNkyk tkuk] LorU=k ?kVuk,¡ gSa vr%
1
igyh ckj iV vkus dh lEHkkouk =
2
1
nwljh ckj iV vkus dh lEHkkouk =
2
1
rhljh ckj iV vkus dh lEHkkouk =
2
1 1 1 1
rhuksa ckj iV vkus dh izkf;drk = × × =
2 2 2 8
mngj.k (Illustration 5) : ,d iklk nks ckj isaQdk tkrk gSA izFke isaQd esa 6 rFkk nwljh isaQd esa ,d fo"ke

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