tasodifiy miqdor va uning taqsimot funksiyasi

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1576320093.doc { } rr = 1 w { } rg = 2 w { } gr = 3 w { } gg = 4 w { } 4 3 2 1 , , , w w w w = w x 0 ) ( = rr x 1 ) ( = rg x 1 ) ( = gr x 2 ) ( = gg x ) ( w x x = w 4 1 ) ( ) ( ) ( ) ( 4 3 2 1 = = = = w w w w p p p p ) ( w x x = { } { } { } 2 1 4 1 4 1 1 3 2 = + = = + = = = w w w w x p p p [ ] t , 0 t w t t ) 0 ( t t £ …

vaqtini belgilasak, bo`ladi. ta`rif. ehtimollik fazosi, o`lchovli fazo (bu yerda , esa dagi borel to`plamlari -algebrasi) bo`lib , , -o`lchovli funksiya bo`lsa, ya`ni ixtiyoriy uchun (1) bo`lsa, funksiyaga tasodifiy miqdor deyiladi. agar chekli bo`lsa, tasodifiy miqdorni uning barcha elementar hodisalardagi qiymatlarini keltirish bilan berish mumkin. masalan 1-misoldagi tasodifiy miqdor 0 1 1 2 0 1 2 yoki ta`rif. agar tasodifiy miqdor chekli yoki sanoqli sondagi qiymatlarnigina qabul qilsa, unga diskret tasoifiy miqdor deyiladi. boshqacha qilib aytganda tasodifiy miqdor diskret deyiladi, agar sonlar ketma-ketligi mavjud bo`lib, , , va bo`lsa. agar barcha qiymatlar va ehtimolliklar ma`lum bo`lsa, ning taqsimot qonuni aniqlangan bo`ladi. jadvalning birinchi qatorida diskret tasodifiy miqdorning qabul qilishi mumkin bo`lgan qiymatlarini, ikkinchi qatorga ularga mos ehtimolliklarni yozsak, … … … … biz diskret tasodifiy miqdorning taqsimot qonunini qatoriga ega bo`lamiz. ixtiyoriy uchun masalan, yuqorida keltirilgan 2-misoldagi tasodifiy miqdorni bunday aniqlab bo`lmaydi. bunday tasodifiy miqdorlarni aniqlash uchun ( ) hodisaning …

hga ega deyiladi. 6˚. taqsimot funksiyaning sakrashlari soni sanoqlidan ko`p emas. isbot. taqsimot funksiyaning dan katta sakrashlari bittadan ko`p bo`laolmaydi, dan gacha bo`lgan sakrashlari 3 tadan ko`p emas, dan gacha sakrashlari dan ko`p bo`lmaydi. bunday ko`rinishdagi taqsimot funksiyaning barcha sakrashlari tartiblab (nomerlab) chiqish mumkin. endi diskret tasodifiy miqdor taqsimot funksiyasi uchun formula keltirib chiqaramiz. agar bo`lsa, , chunki bu holda hodisasi mumkin bo`lmagan hodisa bo`ladi. agar bo`lsa, hodisa faqat va faqat bo`lgandagina ro`y beradi, shuning uchun ham . agar bo`lsa, hodisa va birgalikda bo`lmagan hodisalar yig`indisiga teng bo`ladi va . xuddi shunday bo`lsa, . shunday qilib, diskret tasodifiy miqdorning taqsimot funksiyasi formula bilan aniqlanadi. diskret tasodifiy miqdorning taqsimot funksiyasi oraliqlarda o`zgarmas qiymatlar qabul qiladi va nuqtalarda mos ravishda ehtimollarga teng sakrashlarga ega bo`ladi. endi ma`ruza boshida keltirilgan 1-misoldagi gerb tushishlari soni tasodifiy miqdorning taqsimot funksiyasini topamiz. tasodifiy miqdorning taqsimot qatori 0 1 2 ko`rinishda bo`ladi. agar bo`lsa, ; bo`lsa, ; …

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1576320093.doc { } rr = 1 w { } rg = 2 w { } gr = 3 w { } gg = 4 w { } 4 3 2 1 , , , w w w w = w x 0 ) ( = rr x 1 ) ( = rg x 1 ) ( = gr x 2 ) ( = gg x ) ( w x x = w 4 1 ) ( ) ( ) ( ) ( 4 3 2 1 = = = = w w w w p p p p ) ( w x x = { } { } { } 2 1 4 1 4 1 1 3 2 = …

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