Find a Splice Site in a DNA Sequence 

A DNA sequence consists of base letters A, C, G, and T. Suppose there is a sequence that begins in an exon, contains a splice site, and ends in an intron. If the exons have a uniform base composition, the introns are deficient in C and G, and the splice site consensus nucleotide is G with probability 0.95, the frequency distributions are as follows.

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The state machine has states for exon (1), splice (2), intron (3), and end (4), with the following transition probabilities between states.

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The emissions are nucleotides A (1), C (2), G (3), T (4), or end (5).

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Find the most probable nucleotide subsequence (exon, splice, intron, or end).

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Find the joint probability of the preceding nucleotide sequence and the DNA sequence.

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