bog`lanmagan tajribalar. bernulli formulasi

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1576496276.doc w n n w ) ,... , ( 2 1 n w w w i w i w 4 4 3 4 4 2 1 ta n n w ´ ´ w ´ w = w ... w 3 w 3 2 1 , , е е е s w k ) ( ) ( 2 ) ( 1 ,..., , s k s s a a а æ = ç w = è è è ) ( ) ( ) ( ) ( 2 ) ( 1 , .. s j s i s k s s a a a a a ). , 1 , , 1 , , ( ____ ____ n s n j i j i = = ¹ s i ) ( s i a ) ( ) ( ) ( s i s i a p p = ) ( ) 2 …

tlantiruvchi barcha nuqtalari to`plamini belgilaymiz. ta`rif: agar da har qanday lar uchun tengligi bajarilsa, tajribalar ketma-ketligi bog`lanmagan deyiladi. biz bundan keyin hodisaning ehtimolligi tajribaning tartib raqami ga bog`liq emas deb faraz qilamiz. bu holda deb belgilaymiz. mumkin bo`lgan hollar birgalikda bo`lmagan hodisalarning to`la guruhini tashkil qilganligi uchun bo`ladi. bunday sxema bo`lganda birinchi marta ya.bernulli tomonida qaralganligi uchun, unga bernulli sxemasi deyiladi. bernulli sxemasida odatda deb olinadi. bog`lanmagan tajribalar ketma-ketligi ta`rifidan quyidagi kelib chiqadi. teorema: agar berilgan n ta tajribalar bog`lanmagan bo`lsalar ulardan m tasi ham bog`lanmagan bo`ladi. isboti: deb olamiz. u holda quyidagi munosabat o`rinli bo`ladi . bundan esa ta tajribalar bog`lanmaganliklari uchun bu esa ta tajribaning bolanmaganligini ko`rsatadi. teorema. ta tajribalarning bog`lanmagan bo`lishlari uchun, har qanday va har qanday lar uchun bo`lishi zarur va yetarli. bog`liqmas va bog`liq tajribalarga misollar keltiramiz. 1-misol. tanga tashlanganda gerb tomonini yuqoriga qarab tushish hodisasini, gerb tomonini yuqoriga qarab tushmaslik hodisasini desak, tangani tashlash …

bu bog`lanmagan ta tajribalarda hodisasining rosa m marta, qolgan n-m ta tajribalarda hodisaning ro`y berish ehtimolligini bilan belgilaymiz. ehtimollik uchun formula keltirib chiharamiz. faraz qilaylik a hodisasi burinchi ta tajribada ro`y bersin, qolgan ta tajribada hodisasi ro`y bersin, ya`ni ko`paytirish teoremasiga asosan, bu holning ehtimolligi ga teng bo`ladi. ta tajribalarda hodisaning rosa marta ro`y berishiga imkon tug`diruvchi hollar soni ga teng. qo`shish teoremasiga asosan (1) bu formulaga bernulli formulasi deyiladi. ehtimollar ning binom yoyilmasidagi lar oldidagi koeffitsentlarga teng bo`lganligi uchun ehtimollarga ehtimollikning binomial taqsimot qonuni deyiladi. faraz qilaylik, har bir tajribada ta birgalikda bo`lmagan hodisalarning bittasi ro`y berishi mumkin, har bir tajribada hodisasining ro`y berish ehtimolligi ga teng bo`lsin. ta tajribalarda hodisaning , hodisaning ,…, hodisaning marta ro`y berish ehtimolligini bilan belgilaymiz . bu ehtimollik quyidagiga teng bo`ladi. (2) bu ehtimollik polinomial yoyilmada oldidagi koeffitsentga teng bo`ladi. endi ehtimollikni o`zgarmas da, m ning funksiyasi sifatida o`rganamiz. uchun bernulli formulasiga asosan …

topilsin. bu ehtimolligni topishda bernulli formulasidan foydalansak, bundan ko`rinadiki, katta n lar uchun ehtimollikni bernulli formulasi orqali topish katta texnik qiyinchiliklarga olib kelar ekan. _1302531736.unknown _1306052984.unknown _1306053325.unknown _1306078283.unknown _1307902139.unknown _1307902157.unknown _1306078757.unknown _1306078918.unknown _1306079183.unknown _1306078295.unknown _1306053531.unknown _1306078057.unknown _1306078151.unknown _1306053634.unknown _1306053647.unknown _1306053598.unknown _1306053435.unknown _1306053493.unknown _1306053336.unknown _1306053116.unknown _1306053220.unknown _1306053274.unknown _1306053187.unknown _1306053084.unknown _1306053102.unknown _1306053010.unknown _1302532179.unknown _1302532531.unknown _1302532739.unknown _1302532807.unknown _1302533054.unknown _1302533224.unknown _1302533246.unknown _1302533298.unknown _1302533172.unknown _1302532830.unknown _1302533010.unknown _1302532817.unknown _1302532798.unknown _1302532762.unknown _1302532786.unknown _1302532687.unknown _1302532695.unknown _1302532602.unknown _1302532295.unknown _1302532337.unknown _1302532467.unknown _1302532315.unknown _1302532250.unknown _1302532282.unknown _1302532191.unknown _1302531894.unknown _1302532037.unknown _1302532090.unknown _1302532132.unknown _1302532152.unknown _1302532112.unknown _1302532065.unknown _1302531919.unknown _1302532025.unknown _1302531900.unknown _1302531809.unknown _1302531816.unknown _1302531886.unknown _1302531860.unknown _1302531753.unknown _1302531760.unknown _1302531786.unknown _1302531743.unknown _1302530382.unknown _1302531020.unknown _1302531667.unknown _1302531702.unknown _1302531715.unknown _1302531685.unknown _1302531201.unknown _1302531347.unknown _1302531191.unknown _1302530800.unknown _1302530948.unknown _1302530955.unknown _1302530878.unknown _1302530657.unknown _1302530679.unknown _1302530782.unknown _1302530473.unknown _1302530004.unknown _1302530262.unknown _1302530316.unknown _1302530365.unknown

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1576496276.doc w n n w ) ,... , ( 2 1 n w w w i w i w 4 4 3 4 4 2 1 ta n n w ´ ´ w ´ w = w ... w 3 w 3 2 1 , , е е е s w k ) ( ) ( 2 ) ( 1 ,..., , s k s s a a а æ = ç w = è è è ) ( ) ( ) ( ) ( 2 ) ( 1 , .. s j s i s k s s a a a a a ). , 1 , , 1 , , ( ____ ____ n s n j i …

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