Check if this math is correct SplitInfoAD 414 times log2414

Check if this math is correct? SplitInfo_A(D) = -4/14 times log_2(4/14) - 6/14 times log_2(6/14) - 4/14 times log_2(4/14). = 0.926.

Solution

We have -(4/14)log₂(4/14) –(6/14)log₂(6/14) –(4/14)log₂(4/14) = -(4/14)log₂(4/14) –(4/14)log₂(4/14) –(6/14)log₂(6/14) = -(8/14)log₂ (4/14)- (6/14)log₂(6/14)= -(4/7)log₂(2/7)-(3/7)log₂(3/7).

We know that log_b x = log_a x/log_a b. On using this change of base formula, the given expression changes further to (-4/7)[{log₁₀(2/7)}/{log₁₀(2)}] - (3/7)[ {log₁₀(3/7)}/{log₁₀(2)}] = (-4/7)[ (log₁₀2-log₁₀ 7)/( log₁₀ 2)] -(3/7) [(log₁₀ 3- log₁₀ 7)/(log₁₀ 2)]= -(4/7)[ 1- {(log₁₀ 7)/log₁₀ 2}]- (3/7)[(log₁₀ 3- log₁₀ 7)/(log₁₀ 2)] = -(4/7)[ 1-(0.84509804/0.301029995)] –(3/7)[(0.477121254 -0.84509804)/( 0.301029995)] = (-4/7)*[1-2.807354928] -3/7[ (-0.3679767860)/( 0.301029995)] = -4/7(-1.807354928)-3/7(-1.22392426)= 1.032774245+0.523882468= 1.556656713 = 1.5567 ( on rounding off to 4 decimal places).

Your answer is correct.