Question

Question: For the zero order hidden Markov model defined in homework 3 determine the probability of coding state at the last nucleotide of the sequence AGTAG. Use parameters provided in the homework solution (posted in course content). Show all of your work.

HW3 solution:

Zero order Markov model is described by P(i) = n_i/N,

where

i  = {A,T,G,C},

n_i  – the number of times nucleotide i occurred in the sequence

N – total number of nucleotides in the sequence (sequence length)

P(A)	0.20407
P(T)	0.14379
P(G)	0.35439
P(C)	0.29775

Original sequence used to get above probabilities:

Sequence1_A2 FASTA format

acgcagtcgcagaccgtgacggtggatcagcaagagattttgaacagggccaacgaggtggaggccccgatggcggacccaccgactgatgtccccatcacaccgtgcgaactcacggcggctaaaaacgccgcccaacagctggtattgtccgccgacaacatgcgggaatacctggcggccggtgccaaagagcggcagcgtctggcgacctcgctgcgcaacgcggccaaggcgtatggcgaggttgatgaggaggctgcgaccgcgctggacaacgacggcgaaggaactgtgcaggcagaatcggccggggccgtcggaggggacagttcggccgaactaaccgatacgccgagggtggccacggccggtgaacccaacttcatggatctcaaagaagcggcaaggaagctcgaaacgggcgaccaaggcgcatcgctcgcgcactttgcggatgggtggaacactttcaacctgacgctgcaaggcgacgtcaagcggttccgggggtttgacaactgggaaggcgatgcggctaccgcttgcgaggcttcgctcgatcaacaacggcaatggatactccacatggccaaattgagcgctgcgatggccaagcaggctcaatatgtcgcgcagctgcacgtgtgggctaggcgggaacatccgacttatgaagacatagtcgggctcgaacggctttacgcggaaaacccttcggcccgcgaccaaattctcccggtgtacgcggagtatcagcagaggtcggagaaggtgctgaccgaatacaacaacaaggcagccctggaaccggtaaacccgccgaagcctccccccgccatcaagatcgacccgcccccgcctccgcaagagcagggattgatccctggcttcctgatgccgccgtctgacggctccggtgtgactcccggtaccgggatgccagccgcaccgatggttccgcctaccggatcgccgggtggtggcctcccggctgacacggcggcgcagctgacgtcggctgggcgggaagccgcagcgctgtcgggcgacgtggcggtcaaagcggcatcgctcggtggcggtggaggcggcggggtgccgtcggcgccgttgggatccgcgatcgggggcgccgaatcggtgcggcccgctggcgctggtgacattgccggcttaggccagggaagggccggcggcggcgccgcgctgggcggcggtggcatgggaatgccgatgggtgccgcgcatcagggacaagggggcgccaagtccaagggttctcagcaggaagacgaggcgctctacaccgaggatcgggcatggaccgaggccgtcattggtaaccgtcggcgccaggacagtaaggagtcgaag

Answer 1

Given:-

The original Sequence beased on the Probabilities are computed

P(I)= ni/N where

i= Nucleotides{ A,T,G,C}

ni= Number of times (i) nucleotide occurs in a sequence

N= total number of nucleotides in the sequence

Probabilities of {A,T,G, C}

P(A)	0.20407
P(T)	0.14379
P(G)	0.35439
P(C)	0.29775

We need to determine the probability of coding of the last squence being AGTAG

P(AGTAG)= P(A) x P(G) x P(T) x P(A) x P(G)

= 0.20407 x 0.35439 x 0.14379 x 0.20407 x 0.35439

= .00075206.

End of Answer