Let $\mathrm{A}=\left[\mathrm{a}_{i j} ight]$ be a $2 imes 2$ matrix such that $\mathrm{a}_{i j} \in\{0,1\}$ for all $i$ and $j$. Let the random variable X denote the possible values of the determinant of the matrix $A$. Then, the variance of $X$ is :

Question

Let $\mathrm{A}=\left[\mathrm{a}_{i j}ight]$ be a $2 	imes 2$ matrix such that $\mathrm{a}_{i j} \in\{0,1\}$ for all $i$ and $j$. Let the random variable X denote the possible values of the determinant of the matrix $A$. Then, the variance of $X$ is :

Aicharya · Accepted Answer

$\begin{array}{|c|c|c|c|}
\hline x & 0 & 1 & -1 \\ \hline P(x) & \frac{10}{16} & \frac{3}{16} & \frac{3}{16} \\ \hline
\end{array}$
$\begin{aligned} & \operatorname{Var}(x)=E\left(x^2\right)-[E(x)]^2 \\ & =\sum_{i=1}^3 x_i^2 P\left(x_i\right)-(\mu)^2 \\ & =1 \times \frac{3}{16}+1 \times \frac{3}{16} \quad[\mu=0] \\ & =\frac{6}{16}=\frac{3}{8}\end{aligned}$ /

Let $\mathrm{A}=\left[\mathrm{a}_{i j}\right]$ be a $2 \times 2$ matrix such that $\mathrm{a}_{i j} \in\{0…

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