Maximum likelihood estimation In DNA also known as the Code

Maximum likelihood estimation In DNA, also known as the Code of Life, there exist four different possible bases: adenine (abbreviated A), cytosine (C), guanine (G) and thymine (T). Now, you are given an organism which has a set of unknown DNA base frequencies. Let p_A, p_C, p_G, and p_T be those unknown frequencies. Assume that you obtain a strand of DNA and you want to infer the unknown frequencies. Let n_A, n_C, n_G, n_T be the corresponding number of bases that you observe for A, C, G and T. Please infer the maximum likelihood estimates of the unknown parameters p_A, p_C, p_G, and p_T.

Solution

the max. likelihoood estiamtes of the unkown parameters are

Pa = pa / na

Pc = pc/ nc

Pg = pg / ng

Pt = pt / nt