Neglecting higher powers

We have

f (x) = x − x +

(i) y = y_{1} at x = 0 and

(ii) y = y_{2} at x = ∞, where k, y_{1} and y_{2} are constants, is

The values of a and b are

Area under the pdf curve must be unity 2a + 4a + 4b = 1 2a + 8b = 1.................................................(1) For maximum entropy three region must by equivaprobable thus 2a = 4b = 4b...............................................(2) From (1) and (2) we get b = 1/12 and a = 1/6

The product of Eigen value is equal to the determinant of the matrix. Since one of the Eigen value is zero, the product of Eigen value is zero, thus determinant of the matrix is zero.