= a² - 16a + 64 - 2a² + 6a + 16a - 48 + a² - 6a + 9 = 64 - 48 + 9 = 25
в 4 номере а и а сокращаются+12:4=3 => ответом будет 4b
Найдем для начала ряд распределения случайной величины X
Вычислим для
![k=0,...,3](https://tex.z-dn.net/?f=k%3D0%2C...%2C3)
вероятности ответов на вопрос согласно формуле Бернулли
![P_3(k=0)=C^0_3p^0(1-p)^{3-0}=(1-p)^3=(1-0.9)^3=0.1^3=0.001;\\P_3(k=1)=C^1_3p^1(1-p)^{3-1}=3p(1-p)^2=3\cdot0.9\cdot(1-0.9)^2=0.027 \\ P_3(k=2)=C^2_3p^2(1-p)^{3-2}=3p^2(1-p)=3\cdot 0.9^2\cdot(1-0.9)=0.243 \\ P_3(k=3)=C^3_3p^3(1-p)^{3-3}=p^3=0.9^3=0.729](https://tex.z-dn.net/?f=P_3%28k%3D0%29%3DC%5E0_3p%5E0%281-p%29%5E%7B3-0%7D%3D%281-p%29%5E3%3D%281-0.9%29%5E3%3D0.1%5E3%3D0.001%3B%5C%5CP_3%28k%3D1%29%3DC%5E1_3p%5E1%281-p%29%5E%7B3-1%7D%3D3p%281-p%29%5E2%3D3%5Ccdot0.9%5Ccdot%281-0.9%29%5E2%3D0.027+%5C%5C+P_3%28k%3D2%29%3DC%5E2_3p%5E2%281-p%29%5E%7B3-2%7D%3D3p%5E2%281-p%29%3D3%5Ccdot+0.9%5E2%5Ccdot%281-0.9%29%3D0.243+%5C%5C+P_3%28k%3D3%29%3DC%5E3_3p%5E3%281-p%29%5E%7B3-3%7D%3Dp%5E3%3D0.9%5E3%3D0.729)
Функция распределения:
![F(X)=\begin{cases} & \text{ } 0,~~~~~~~ x \leq 0\\ & \text{ } 0.001,~~~0\ \textless \ x \leq 1 \\ & \text{ } 0.028,~~~ 1\ \textless \ x \leq 2\\ & \text{ } 0.271,~~~ 2\ \textless \ x \leq 3 \\ & \text{ } 1,~~~~~~~x\ \textgreater \ 3 \end{cases}](https://tex.z-dn.net/?f=F%28X%29%3D%5Cbegin%7Bcases%7D%0A+%26+%5Ctext%7B++%7D+0%2C~~~~~~~+x+%5Cleq+0%5C%5C+%0A+%26+%5Ctext%7B++%7D+0.001%2C~~~0%5C+%5Ctextless+%5C+x+%5Cleq+1+%5C%5C+%0A+%26+%5Ctext%7B++%7D+0.028%2C~~~+1%5C+%5Ctextless+%5C+x+%5Cleq+2%5C%5C+%0A+%26+%5Ctext%7B++%7D+0.271%2C~~~+2%5C+%5Ctextless+%5C+x+%5Cleq+3+%5C%5C+%0A+%26+%5Ctext%7B++%7D+1%2C~~~~~~~x%5C+%5Ctextgreater+%5C+3+%0A%5Cend%7Bcases%7D)
Математическое ожидание:
![M(X)=np=3\cdot 0.9=2.7](https://tex.z-dn.net/?f=M%28X%29%3Dnp%3D3%5Ccdot+0.9%3D2.7)
Дисперсия:
![D(X)=np(1-p)=3\cdot0.9\cdot0.1=0.27](https://tex.z-dn.net/?f=D%28X%29%3Dnp%281-p%29%3D3%5Ccdot0.9%5Ccdot0.1%3D0.27)
Среднее квадратическое отклонение:
![\sigma(X)= \sqrt{D(X)} = \sqrt{0.27} =0.3 \sqrt{3}](https://tex.z-dn.net/?f=%5Csigma%28X%29%3D+%5Csqrt%7BD%28X%29%7D+%3D+%5Csqrt%7B0.27%7D+%3D0.3+%5Csqrt%7B3%7D+)