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Let A = [aij] be a 2 2 matrix such that aij \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:
(4) 38
X=a11a22-a12a21; total 24=16 matrices
X=1: a11=a22=1, (a12,a21) (1,1) ⇒ 3 matrices; X=-1: 3 matrices; X=0: 10
E(X)=0 (symmetric) ⇒ Var(X)=E(X2)= 3+316
∴ Var(X)= 38
Answer: (4)
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