Laboratoriya ishi №2 Mavzu: Bernulli, Puasson formulalari, Muavr-Laplasning lokal va integral teoremalari. Laboratoriya mashgʻulotida bajariladigan vazifalari

Laboratoriya ishi № 2

Mavzu: Bernulli, Puasson formulalari, Muavr-Laplasning lokal va integral teoremalari.

Laboratoriya mashgʻulotida bajariladigan vazifalari:

2.1-masala. n ta erkli sinovning har birida A hosianing ro’y berish ehtimoli p. A hodisaning n ta tajribada:

1. Roppa-rosa k₁ marta ro’y berishi ehtimolini toping: P_n(X=k₁)-?

2. Kamida k₁ ko’pi bilan k₂ marta ro’y berish ehtimoli topilsin.

3. Ko’pi bilan k₃ marta ro’y berish ehtimoli topilsin.

4. Kamida k₄ marta ro’y berish ehtimoli topilsin.

5. Hech bo’lmaganda bir marta ro’y berish ehtimoli topilsin.

6. A hodisaning eng ehtimolli ro’y berishlar soni aniqlansin.

N, p, k₁, k₂, k₃, k₄ parametrlarni quyidagi formulalardan aniqlang:

V = 15;

P = 0,3 + 15/100 = 0,45

N = 10, K₁ = 5, K₂ = 8, K₃ = 7, K₄ = 6

Yechish:

1. P₁₀ (x=5) =

2. P₁₀(5<=x<=8) = P₁₀(x=5) + P₁₀(x=6) + P₁₀(x=7) + P₁₀(x=8) =0.234+0.109+0.052+0.0097=0.4047

3. P₁₀(0<=x<=7) = P₁₀(x=0) + P₁₀(x=1) + P₁₀(x=2) + P₁₀(x=3)+ P₁₀(x=4) + P₁₀(x=5) + P₁₀(x=6) + P₁₀(x=7) = 0.006+0.04+0.122+0.215+0.253+0.234+0.109+0.052+0.0097=