Let A = [ a ij ] be a 2 × 2 matrix such that a ij ∈ { 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 A = [ a ij ​ ] be a 2 × 2 matrix such that a ij ​ ∈ { 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 :

TestHub · Accepted Answer

x P ( x ) ​ 0 16 10 ​ ​ 1 16 3 ​ ​ − 1 16 3 ​ ​ ​ ​ Var ( x ) = E ( x 2 ) − [ E ( x ) ] 2 = i = 1 ∑ 3 ​ x i 2 ​ P ( x i ​ ) − ( μ ) 2 = 1 × 16 3 ​ + 1 × 16 3 ​ [ μ = 0 ] = 16 6 ​ = 8 3 ​ ​

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