EHTIMOLLAR NAZARIYASI FANIDAN YAKUNIY NAZORAT TEST SAVOLLARI Kunning bulutsiz bo’lish ehtimolligi p=0.8 ga teng. Kunning yog’imgarchilik bo’lish ehtimolligini toping.
0,2 B) 0,5 C) 0 D) 1
Ikki kub tashlandi. Chiqqan ochkolar yig’indisi 3 ga karrali bolish ehtimolligini toping.
1/18 B) 1/12 C) 1/3 D) 1/36
Ikki kub tashlandi. Chiqqan ochkolar yig’indisi 4 ka karrali bo’lish ehtimolligini toping.
1 B) 1/4 C) 1/2 D) 1/9
Quyidagi tengliklardan qaysi biri bog’liq hodisalarning ehtimolliklarini kopaytirish teoremasini ifodalaydi?
P(AB)=P(A)P(B)
P(AB)=0
P(AB)=P(VA)
P(AB)=P(A)P(B/A)
1 B) 2 C) 3 D) 4
Quyida tengliklardan qay biri bog’liq bolmagan hodisalarning ehtimolliklarini qoshish teoremasini ifodalaydi?
P(A+B)=P(A)+P(B)
P(A+B)=0
P(A+B)=P(A)+P(B)-P(AB)
P(A+B)=1
P(A+B)=P(B)
1 B ) 2 C) 3 D)4
Muqarrar hodisaning ehtimolligi nechaga teng
0 ga B) 1ga C) 2 ga D) har hil bolishi mumkin
Mumkin bolmagan hodisaning ehtimolligi nechaga teng
0 ga B) 1ga C) 2 ga D) har hil bolishi mumkin
Tasodifiy hodisaning ehtimolligi qaysi oraliqqa tegishli?
(0,1) B) (-1,0) C) (-1,1) D) barcha musbat sonlar bolishi mumkin
A hodisaning B hodisa roy berganligi shartli ehtimolligi formulasi qaysi javobda tog’ri ko’rsatilgan
P(A+B)=P(A)+P(B)
P(AB)=P(A/B)P(B)
F(b)-F(a)=
P(A/B)=P(AB)/P(B)
Ikkita birgalikta bo’lmagan hodisalar yig’indisining ehtimolligi nimaga teng?
P(A+B)=P(A)+P(B)
P(AB)=P(A/B)P(B)
P(A+B)=P(A)+P(B)-P(AB)
0 ga teng
Ikkita birgalikta bo’lgan hodisalar yig’indisi ehtimolligi nimaga teng?
P(A+B)=P(A)+P(B)
P(AB)=P(A/B)P(B)
P(A+B)=P(A)+P(B)-P(AB)
0 ga teng
Bernulli formulasini korsating
P(A+B)=P(A)+P(B)
P(AB)=P(A/B)P(B)
P(A+B)=P(A)+P(B)-P(AB)
Pn(k)=
Tajribalar soni etarlicha katta bolganda hodisaning n ta tajribada roppa rosa k marta roy berishi ehtimolligini taqribiy hisoblash uchun qaysi teorema qollaniladi?
Bernulli
Puasson teoremasi
Laplas lokal funksiyasi qanday funksiya?
Toq
Juft
Toqta emas, juftta emas
Toq bolisji ha’m , juft bolishi ham mumkin
Ehtimolliklarning binomial taqsimoti dep nimaga aytiladi?
Bernulli formulasi bilan aniqlanadigan ehtimolliklar taqsimotiga aytiladi.
Laplasning integral formulasi bilan aniqlanadigan ehtimolliklar taqsimotiga aytiladi
Puasson formulasi bilan aniqlanadigan ehtimolliklar taqsimotiga aytiladi
Sinov natijasida roy berishi mumkin bolgan har qanday fakt bu .....
Ehtimollik B) hodisa C) tajriba D) elementar hodisa
Sinovning har qanday natijasi ...... ?
Muqarrar hodisa
B) mumkin bolmagan
Qarama-qarshi hodisa
Elementar hodisa
Agar sinov natiyjasida bir nechta hodisalardan faqat bittasi roy bersa ular ........ deyiladi
Qarama-qarshi hodisalar
Hodisalar tola guruhi tashkil etiladi
Teng imkoniyatli hodisalar
Muqarrar hodisalar
Agar A va B hodisalardan birining roy berishi ikkinchisining roy berish yoki roy bermasligiga tasir etmasa u hodisalar .......... deyiladi
Bog’liq bolmagan
Bog’liq
Birgalikta
Birgalikta bolmagan
Tavakkaliga 20 dan katta bolmagan natural son tanlanganda uning 5 ka karrali bolishi ehtimolligini toping
0.1 B) 0.2 C) 0.3 D) 0.4
Tavakkaliga 20 dan katta bolmagan natural son tanlanganda uning 3 ka karrali bolishi ehtimolligini toping
0.1 B) 0.2 C) 0.3 D) 0.4
Tavakkaliga 20 dan katta bolmagan natural son tanlanganda uning 4 ka karrali bolishi ehtimolligini toping
A) 0.5 B) 0.2 C) 0.3 D) 0.4
Ikkita oyin soqqasi barabar tashlanganda tushgan ochkolar yig’indisi 8 ga ten’ bolishi ehtimolligini toping
6/36 B) 5/36 C) 7/36 D) 5/18
Ikkita oyin soqqasi barabar tashlanganda tushgan ochkolar kopaytmasi 8 ga ten bolishi ehtimolligini toping
A) 1/36 B) 7/18 C) 1/18 D) 5/18
Tavakkaliga 20 dan katta bolmagan natural son tanlanganda uning 20 ning boluvchisi bo’lish ehtimolligin toping.
A) 0.1 B) 0.2 C) 0.3 D) 0.4
Bayes formulasini korsating
PA(Bk) =
P(A+B)=P(A)+P(B)
PA(Bk) =
D)PA(Bk) =
Har birida hodisaning roy berishi ehtimolligi p ga teng n ta bogliqmas sinovlarda hodisaning rossa m marta roy berish ehtimolligi
Bernulli formulasi
Laplasning lokal teoremasi
Laplasning integral teoremasi
Puasson teoremasi
Har birida hodisaning roy berishi ehtimolligi p ga teng n(katta n larda) ta bogliqmas sinovlarda hodisaning kamida m1 marta kopi bilan m2 marta roy berish ehtimolligi
Bernulli formulasi
Laplasning lokal teoremasi
Laplasning integral teoremasi
Puasson teoremasi
Katta n lar va kichik p larda qaysi teorema orinli?
Bernulli formulasi
Laplasning lokal teoremasi
Laplasning integral teoremasi
Puasson teoremasi
Qaysi shartda Laplasning formulasi qullash mumkin?
npq>20
npq=20
npq<10
npq>10
Sinov natijasida oldindan malum bo’lgan qiymatlardan birini qabul qiladigan miqdor ………. deyiladi.
Aniq miqdor
Tasodifiy miqdor
Taqribiy miqdor
Aniq emas miqdor
Chekli yoki cheksiz sonli ketma-ketkliklardan iborat miqdorga .............. tasodifiy miqdor deyiladi.
Diskret
uzluksiz
Aniq
Toliq
X diskret tasodifiy miqdor nechta turda berilishi mumkin?
3
4
2
5
X diskret tasodifiy miqdorning taqsimot qonuni qanday usullarda beriladi?
Rasm , grafik, formula
Jadval, analitik, rasm
Jadval, analitik, grafik
Jadval, analitik, formula
X diskret tasodifiy miqdorning [a,b] oraliqdagi qiymatlarini qabul qilish ehtimolligi taqsimot funksiyasining bu oraliqdagi orttirmasi qaysi formula orqali ifodalanadi?
F(x)=F(a)+F(b)
F(x)=F(a-b)+F(a+b)
F(x)=F(a+b)-F(a-b)
F(x)=F(b)-F(a)
Binomial taqsimotini aniqlash uchun qaysi formuladan foydalanamiz?
Bernulli formulasi
Laplasning lokal teoremasi
Laplasning integral teoremasi
Puasson teoremasi
Puasson taqsimotini aniqlash uchun qaysi formuladan foydalanamiz?
Bernulli formulasi
Laplasning lokal teoremasi
Laplasning integral teoremasi
Puasson teoremasi
Birorta chekli yoki cheksiz oraliqdagi barcha qiymatlarni qabul qilishi mumkin bolgan tasodifiy miqdor ............. tasodifiy miqdor deyiladi
Diskret
Uzlikli
Uzliksiz
Toliq
Uzliksiz tasodifiy miqdorlar kop hollarda qanday funksiyalar ko’rinishida beriladi?
Integral, chiziqli
Hosilaviy, egrichiziq
Integral, differentsial
Chiziqli, differentsial
X uzliksiz tasodifiy miqdor ehtimolliklarining ............... dep taqsimot funksiyasi F(x) ning birinchi tartibli hosilasi f(x) funksiyaga aytiladi.
Taqsimot zichligi
Taqsimot funksiyasi
Integral funksiyasi
Lokal funksiyasi
X uzliksiz tasodifiy miqdorning (a,b) oraliqqa tegishli qiymatni qabul qilishi ehtimolligi formulasini ko’rsating
P(a P(b P(a P(a Zichlik funksiyasi f(x) ning hossalaridan birini korsating
f(x)<0
f(x) 0
f(x)=0
f(x)<-1
Zichlik funksiyasi - dan + gacha oraliqda olingan hosmas integral ...... teng
-1
0
1
-2
X diskret tasodifiy miqdorning ................ dep uning mumkin bolgan barcha qiymatlarini ularning ehtimolliklariga kopaytmalari yig’indisiga teng songa aytiladi.
Analitik funksiyasi
Grafigi
Matematik kutilishi
Geometrik sathi
Matematik kutilish qaysi kurinishda ifodalanadi?
M(X)
D(X)
A(X)
C(X)
O’zgarmas miqdorning matematik kutilishi nimaga teng ?
M(C)=1
M(C)=C
M(C)=-1
M(C)=0
Tasodifiy miqdorlar yig’indisining matematik kutilishini ko’rsating
M(X+Y)=M(X)+M(Y)-M(XY)
M(X+Y)=M(X)+M(Y)
M(X+Y)=M(X-Y)+M(Y)
M(XY)=M(X)M(Y)
Tasodifiy miqdorlar kopaytmasining matematik kutilishini ko’rsating
A)M(X+Y)=M(X)+M(Y)-M(XY)
B)M(X+Y)=M(X)M(Y)
C)M(X+Y)=M(X-Y)M(Y)
M(XY)=M(X)M(Y)
X tasodifiy miqdorning ............... deb tasodifiy miqdorning uzining matematik kutilishidan chetlanishi kvadratining matematik kutilishiga aytiladi.
Kvadrati
Ikkilangani
Dispersiyasi
Qiymati
Dispersiya miqdorini qaysi formula boyicha aniqlaymiz?
D(X)=M(X2) – (M(X))2
D(X)=M(X) – (M(X))2
D(X)=M(X2) – M(X)
D(X)=M(X2) + (M(X))2 O’zgarmasning dispersiyasi ....... teng.
1 ga
-1 ga
0 ga
2 ga
Bog’liqmas tasodifiy miqdorlar yig’indisining dispersiyasi qanday aniqlanadi?
D(X+Y)=D(X)D(Y)+D(X)
D(X+Y)=D(X)+D(Y)
D(X)=M(X2) – (M(X))2
D(X+Y)=D(X)-D(Y)
Diskret tasodifiy miqdorning binomial taqsimotining matematik kutilishini korsating
M(X)=np
ommaviy bir jinsli tasodifiy hodisalarning qonuniyatlarini
muqarrar va mumkin bo’lmagan hodisalarning qonuniyatlarini
har qanday tasodifiy hodisalarning qonuniyatlarini
Ehtimollik klassik ta’rifidagi n:
imkon tug’diruvchi hollar soni
elementar hodisalarming barcha soni
m dan katta bo’lgan ixtiyoriy son
har doim n=m
Qarama-qarshi hodisalar yig’indisi nimaga teng ?
1
2
0
-1
Klassik ehtimollik formulasini ko’rsating
P=m/n
P=mn
P=n/m
P=n2/m
P(U)=1 bu qanday hodisa ?
Tasodifiy
Aniq
Muqarrar hodisa
Aniq emas hodisa
0 bu qanday ehtimollik ?
Tasodifiy
Aniq
Muqarrar ehtimollik
Aniq emas ehtimollik
P(A)=0 bu qanday ehtimollik ?
Tasodifiy
Aniq
Muqarrar ehtimollik
Mumkin bolmagan ehtimollik
Geometrik ehtimollik formulasini korsating
P=S1/S2
P=m1/m2
P(A)=mesD1/mesD2
P(A)=mesD1mesD2
Agar sinovlar natijalarining har qanday kombinatsiyasi bog’liqmas hodisalar toplamidan iborat bolsa, bu sinovlar .......... deyiladi.
Muqarrar
Bog’liqmas
Uzliksiz
Diskret
Chekli sondagi n ta ketma-ket bog’liqmas sinovlar natijasida bir hodisa roy berishi mumkin bolsa bunday ketma-ketlik ....... deyiladi
Laplas lokal teoremasi
Bernulli sxemasi
Puasson teoremasi
Laplas integral teoremasi
Qutida 3 ta oq 2 ta qora shar bor. Qutidan olinga 3 ta sharning qora bolish ehtimolligini toping?
1
0.5
0.37
0
Qutida 3 ta oq shar bor . Olingan 3 ta sharning oq bolish ehtimolligi qancha ?
0
0.1
30 dan katta bolmagan son oylanganda 6 ga karrali bolish ehtimolligini toping
A) 1/4
B) 1/5
C) 1/6
D) 1/7
30 dan katta bolmagan son oylanganda 9 ga karrali bolish ehtimolligini toping
A) 0.33 B) 0.5 C) 0.1 D) 0.01
30 dan katta bolmagan son oylanganda 5 ga karrali bolish ehtimolligini toping
A)0.33 B) 0.5 C) 0.7 D) 0.2
30 dan katta bolmagan son oylanganda 7 ga karrali bolish ehtimolligini toping
A)2/15 B) 2/5 C) 1/17 D) 0.01
30 dan katta bolmagan son oylanganda 8 ga karrali bolish ehtimolligini toping
A)0.33 B) 0.5 C) 0.7 D) 0.1
30 dan katta bolmagan son oylanganda 10 ga karrali bolish ehtimolligini toping
A)0.1 B) 0.5 C) 0.7 D) 0.01
30 dan katta bolmagan son oylanganda juft bolish ehtimolligini toping
A)0.33 B) 0.5 C) 0.7 D) 0.01
30 dan katta bolmagan son oylanganda 3 ga karrali bolish ehtimolligini toping
A)1/3 B) 1/5 C) 0.7 D) 0.01
30 dan katta bolmagan son oylanganda toq son bolish ehtimolligini toping
A)0.5 B) 0.56 C) 0.7 D) 0.01
40 dan katta bolmagan son oylanganda juft son bolish ehtimolligini toping
A)0.33 B) 0.5 C) 0.7 D) 0.65
40 dan katta bolmagan son oylanganda toq son bolish ehtimolligini toping
A)0.33 B) 0.77 C) 0.5 D) 0.65
40 dan katta bolmagan son oylanganda 3 ga karrali bolish ehtimolligini toping
A)13/20 B) 15 /40 C) 13/40 D) 0.01
40 dan katta bolmagan son oylanganda 5 ga karrali bolish ehtimolligini toping
A)0.1 B) 0.5 C) 0.7 D) 0.2
40 dan katta bolmagan son oylanganda 6 ga karrali bolish ehtimolligini toping
A)3/40 B) 3/20 C) 0.7 D) 0.01
40 dan katta bolmagan son oylanganda 7 ga karrali bolish ehtimolligini toping
A)0.12 B) 0.25 C) 0.7 D) 0.125
40 dan katta bolmagan son oylanganda 8 ga karrali bolish ehtimolligini toping
A)0.125 B) 0.5 C) 0.7 D) 0.01
40 dan katta bolmagan son oylanganda 4 ga karrali bolish ehtimolligini toping
A)0.1 B) 0.25 C) 0.7 D) 0.01
40 dan katta bolmagan son oylanganda 9 ga karrali bolish ehtimolligini toping
A)0.1 B) 0.5 C) 0.7 D) 0.01
40 dan katta bolmagan son oylanganda 10 ga karrali bolish ehtimolligini toping
A)0.1 B) 0.5 C) 0.7 D) 0.01
40 dan katta bolmagan son oylanganda 12 ga karrali bolish ehtimolligini toping
A)0.15 B) 12/40 C) 0.075 D) 3/40
40 dan katta bolmagan son oylanganda 13 ga karrali bolish ehtimolligini toping
A)3/40 B) 5/40 C) 3/20 D) 12/40
40 dan katta bolmagan son oylanganda 15 ga karrali bolish ehtimolligini toping
A)0.1 B) 0.05 C) 0.7 D) 0.01
1 dan 100 gacha sonlar ichidan son tanlanganda 1 raqami bo’lishi ehtimolini toping ?
0.5 B) 0.3 C) 0.2 D) 0.25
1 dan 100 gacha sonlar ichidan son tanlanganda 2 raqami bo’lishi ehtimolini toping ?
0.2 B) 0.3 C) 0.7 D) 0.25
1 dan 100 gacha sonlar ichidan son tanlanganda 3 raqami bo’lishi ehtimolini toping ?
A) 0.5 B) 0.3 C) 0.6 D) 0.2
1 dan 100 gacha sonlar ichidan son tanlanganda 4 raqami bo’lishi ehtimolini toping ?
A)0.5 B) 0.3 C) 0.2 D) 0.25
1 dan 100 gacha sonlar ichidan son tanlanganda 5 raqami bo’lishi ehtimolini toping ?
A)0.2 B) 0.3 C) 0.22 D) 0.25
1 dan 100 gacha sonlar ichidan son tanlanganda 6 raqami bo’lishi ehtimolini toping ?
A)0.5 B) 0.3 C) 0.2 D) 0.25
1 dan 100 gacha sonlar ichidan son tanlanganda 8 raqami bo’lishi ehtimolini toping ?
A)0.5 B) 0.3 C) 0.2 D) 0.25
1 dan 100 gacha sonlar ichidan son tanlanganda 9 raqami bo’lishi ehtimolini toping ?
0.5 B) 0.2 C) 0.4 D) 0.25
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.5 va 0.4. Ikkitasi ham tekkizish ehtimolligini toping
0.2
0.9
0.1
0.4
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.6 va 0.4. Ikkitasi ham tekkizish ehtimolligini toping
A) 0.2
0.9
0.24
0.4
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.8 va 0.9. Ikkitasi ham tekkizish ehtimolligini toping
A) 0.2
0.9
0.1
0.72
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.2 va 0.7. Ikkitasi ham tekkizish ehtimolligini toping
A)0.2
0.9
0.14
0.4
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.1 va 0.9. Ikkitasi ham tekkizish ehtimolligini toping
0.2
0.7
0.09
0.4.
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.1 va 0.9. Ikkitasi ham tekkiza olmaslik ehtimolligini toping
0.2
0.7
0.09
0.4
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.8 va 0.5. Ikkitasi ham tekkiza olmaslik ehtimolligini toping
0.2
0.01
0.02
0.4
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.5 va 0.5. Ikkitasi ham tekkiza olmaslik ehtimolligini toping
0.2
0.7
0.25
0.4
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.7 va 0.4. Ikkitasi ham tekkiza olmaslik ehtimolligini toping
0.2
0.7
0.09
0.18
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.4 va 0.2. Ikkitasi ham tekkiza olmaslik ehtimolligini toping
0.48
0.7
0.09
0.4
Ikkita merganning nishonga tekkizish ehtimolligi mos ravishda 0.3 va 0.5. Ikkitasi ham tekkiza olmaslik ehtimolligini toping
0.2
0.7
0.35
0.4
Gol urish ehtimolligi p=0.25 bolsa . Gol urmaslik ehtimolligini toping ?
0.75 B) 0.85 C) 0.45 D)0.1
Gol urish ehtimolligi p=0.6 bolsa . Gol urmaslik ehtimolligini toping ?
A) 0.7 B) 0.85 C) 0.4 D)0.1
Quyidagi mulohozalardan tog’risini toping
1.Qarama qarshi ehtimolliklar yigindisi 0 ga teng
2. Tanganing bir tomoni chiqish ehtimoli 1 ga teng
3. Klassik ehtimollik formulasi P(A)=m/n
A) 1,2 B) 1,2,3 C) 3 D) togri javob yoq
Ikki basketbolchining savatga top tushirish ehtimolligi mos ravishda 0.6 va 0.5 ga teng ularning faqat 1 chisi tushirish ehtimolligini toping.
0.4
0.3
0.25
0.5
Ikki basketbolchining savatga top tushirish ehtimolligi mos ravishda 0.4 va 0.7 ga teng ularning faqat 1 chisi tushirish ehtimolligini toping.
0.12
0.2
0.25
0.5
Ikki basketbolchining savatga top tushirish ehtimolligi mos ravishda 0.2 va 0.8 ga teng ularning faqat 1 chisi tushirish ehtimolligini toping.
0.4
0.2
0.25
0.04
Ikki basketbolchining savatga top tushirish ehtimolligi mos ravishda 0.1 va 0.6 ga teng ularning faqat 1 chisi tushirish ehtimolligini toping.
0.4
0.2
0.04
0.5
Ikkita uyin soqqasi birgalikta tashlanganda ikkalasi ham bir xil bolish ehtimolligini toping.