a m p ; ∣ A ∣ = ∣ a 11 a m p ; a 12 a 21 a m p ; a 22 ∣ a m p ; = a 11 a 22 − a 21 a 12 a m p ; = { − 1 , 0 , 1 } \begin{aligned}& |A|=\left|\begin{array}{ll}a_{11} & a_{12} \\a_{21} & a_{22}\end{array}\right| \\& =a_{11} a_{22}-a_{21} a_{12} \\& =\{-1,0,1\}\end{aligned} am p ; ∣ A ∣ = a 11 a 21 am p ; a 12 am p ; a 22 am p ; = a 11 a 22 − a 21 a 12 am p ; = { − 1 , 0 , 1 }
x a m p ; P i a m p ; P i X i a m p ; P 1 X i 2 − 1 a m p ; 3 16 a m p ; − 3 16 a m p ; 3 16 0 a m p ; 10 16 a m p ; 0 a m p ; 0 1 a m p ; 3 16 a m p ; 3 16 a m p ; 3 16 a m p ; a m p ; ∑ P i X i = 0 a m p ; ∑ P i X i 2 = 3 8 \begin{array}{c|c|c|c}\mathrm{x} & \mathrm{P}_{\mathrm{i}} & \mathrm{P}_{\mathrm{i}} \mathrm{X}_{\mathrm{i}} & \mathrm{P}_1 \mathrm{X}_{\mathrm{i}}{ }^2 \\-1 & \frac{3}{16} & -\frac{3}{16} & \frac{3}{16} \\0 & \frac{10}{16} & 0 & 0 \\1 & \frac{3}{16} & \frac{3}{16} & \frac{3}{16} \\\hline & & \sum \mathrm{P}_{\mathrm{i}} \mathrm{X}_{\mathrm{i}}=0 & \sum \mathrm{P}_{\mathrm{i}} \mathrm{X}_{\mathrm{i}}{ }^2=\frac{3}{8}\end{array} x − 1 0 1 am p ; P i am p ; 16 3 am p ; 16 10 am p ; 16 3 am p ; am p ; P i X i am p ; − 16 3 am p ; 0 am p ; 16 3 am p ; ∑ P i X i = 0 am p ; P 1 X i 2 am p ; 16 3 am p ; 0 am p ; 16 3 am p ; ∑ P i X i 2 = 8 3
a m p ; ∴ var ( x ) = ∑ P i X i 2 − ( ∑ P i X i ) 2 a m p ; = 3 8 − 0 = 3 8 \begin{aligned}& \therefore \operatorname{var}(\mathrm{x})=\sum \mathrm{P}_{\mathrm{i}} \mathrm{X}_{\mathrm{i}}^2-\left(\sum \mathrm{P}_{\mathrm{i}} X_{\mathrm{i}}\right)^2 \\& =\frac{3}{8}-0=\frac{3}{8}\end{aligned} am p ; ∴ var ( x ) = ∑ P i X i 2 − ( ∑ P i X i ) 2 am p ; = 8 3 − 0 = 8 3