First time job P30 (5)

5. Consider the following sequence:

Atgcttaacgtgcttaacctgaagcttccgctgaagaacctg

Ctgaacccgcttaagcttaagctgaaccttctgaacctgctt

(a) Estimating each probability value based on this sequence and calculating the first, second, Sankai and four order entropy of the sequence.

Solution : (a) According to test instructions:

P (A) =21/84=0.25 P (T) =22/84=0.27 P (G) =16/84=0.19 P (C) =24/84=0.28

So the first-order entropy is:

H=-log2 (0.25) * 0.25-LOG2 (0.27) * 0.27-LOG2 (0.19) * 0.19-LOG2 (0.28) * 0.28

= 0.5 + 0.51+ 0.46+ 0.51

=1.98

First time job P30 (5)