Let A = [ a _ i j ] be a 2 2 matrix such that a _ i j 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 :

Step-by-step solution

array |c|c|c|c| x & 0 & 1 & -1 P(x) & 10 16 & 3 16 & 3 16 array aligned & Var (x)=E (x^2 )-[E(x)]^2 & = _ i=1 ^3 x_i^2 P (x_i )-( )^2 & =1 3 16 +1 3 16 [ =0] & = 6 16 = 3 8 aligned